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Continuity Theory 1st ed. 2016 [Kõva köide]

  • Formaat: Hardback, 460 pages, kõrgus x laius: 235x155 mm, kaal: 9264 g, 110 Illustrations, black and white; XIX, 460 p. 110 illus., 1 Hardback
  • Ilmumisaeg: 14-Jun-2016
  • Kirjastus: Springer International Publishing AG
  • ISBN-10: 3319311581
  • ISBN-13: 9783319311586
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Continuity Theory 1st ed. 2016Suurem pilt
  • Formaat: Hardback, 460 pages, kõrgus x laius: 235x155 mm, kaal: 9264 g, 110 Illustrations, black and white; XIX, 460 p. 110 illus., 1 Hardback
  • Ilmumisaeg: 14-Jun-2016
  • Kirjastus: Springer International Publishing AG
  • ISBN-10: 3319311581
  • ISBN-13: 9783319311586
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9783319311586.html
Märksõnad:
This book presents a detailed, self-contained theory of continuous mappings. It is mainly addressed to students who have already studied these mappings in the setting of metric spaces, as well as multidimensional differential calculus. The needed background facts about sets, metric spaces and linear algebra are developed in detail, so as to provide a seamless transition between students" previous studies and new material.  In view of its many novel features, this book will be of interest also to mature readers who have studied continuous mappings from the subject"s classical texts and wish to become acquainted with a new approach. The theory of continuous mappings serves as infrastructure for more specialized mathematical theories like differential equations, integral equations, operator theory, dynamical systems, global analysis, topological groups, topological rings and many more. In light of the centrality of the topic, a book of this kind fits a variety of applications, espec

ially those that contribute to a better understanding of functional analysis, towards establishing an efficient setting for its pursuit.

Overview.- General Preparation.- Continuity Enabling Structures.- Construction of New Spaces.- Various Kinds of Spaces.- Fundamentals of Linear Continuity.- Basic Categorical Concepts.- The Category C .- Reflective Categories of C .- Enriched Dualities.- The Category CV .- Reflective Subcategories of CV .- Linear Continuous Representations.- Smooth Continuity.- Supplementary Reading.

Arvustused

This book is devoted to the so-called continuity theory, which includes continuous mappings between topological, metric and convergence spaces. Primarily, the book is designed for students, but it also contains some information which could be interesting for advanced readers. In conclusion, the book contains very interesting and somewhat unusual treatments of continuity. (Vesko Valov, Mathematical Reviews, August, 2017)

The author presents the theory of continuous mappings, mainly in the realm of convergence spaces . contains many exercises and a section on supplementary reading. The work is addressed to readers who have studied continuous mappings in the metric setting, as well as multidimensional differential calculus. book will mainly be studied and used by mature readers and lecturers, who will appreciate the wealth of information that it provides, much of which is not available in book form elsewhere. (Hans Peter Künzi, zbMATH 1350.54001, 2017)

1 Overview
1(16)
1.1 Ways to Express Continuity
1(3)
1.2 Categorical Concepts
4(7)
1.3 Enriched Functional Analysis
11(6)
2 General Preparation
17(36)
2.1 About Sets
17(3)
2.1.1 Axioms for Sets
18(1)
2.1.2 Set Building
19(1)
2.2 Functions
20(4)
2.2.1 Anatomy of Functions
20(1)
2.2.2 Function Related Concepts
21(3)
2.3 Indexed Set Building
24(3)
2.3.1 Constructions with Indexed Families of Sets
24(2)
2.3.2 Images and Preimages of Families
26(1)
2.4 Relations
27(4)
2.4.1 Relation Concept
27(1)
2.4.2 Ordered and Preordered Sets
27(2)
2.4.3 Ordinals and Transfinite Induction
29(2)
2.5 The Class of All Sets
31(5)
2.5.1 Getting Around Russell's Paradox
31(1)
2.5.2 The Class S of Functions Between Sets
32(2)
2.5.3 Factorizations of Functions
34(2)
2.6 Basic Algebraic Structures
36(5)
2.6.1 Monoid Related Structures
36(3)
2.6.2 Number Fields
39(2)
2.7 Vector Spaces and Linear Mappings
41(12)
2.7.1 Vector Space Concept
41(4)
2.7.2 Linear Mapping Concept
45(1)
2.7.3 Factorization of Linear Mappings
46(1)
2.7.4 Quotient Vector Spaces
46(1)
2.7.5 Cartesian Products of Vector Spaces
47(1)
2.7.6 Vector Spaces of Linear Mappings
48(1)
2.7.7 Interdependence of Real and Complex Linear Functionals
48(1)
2.7.8 Free Vector Spaces
49(4)
3 Continuity Enabling Structures
53(40)
3.1 Real Intervals
53(10)
3.1.1 Convergent Sequences in Real Intervals
53(2)
3.1.2 Filters
55(2)
3.1.3 Filter Convergence in R
57(2)
3.1.4 Completeness of the Real Line
59(1)
3.1.5 Continuous Mappings Between Real Intervals
60(3)
3.2 Metric Spaces
63(12)
3.2.1 Normed Spaces
63(1)
3.2.2 Metric Space Concept
64(1)
3.2.3 Auxiliary Concepts for Metric Spaces
65(1)
3.2.4 Convergence in Metric Spaces
66(1)
3.2.5 Complete Metric Spaces
67(3)
3.2.6 Continuous Mappings Between Metric Spaces
70(1)
3.2.7 Cartesian Products of Metric Spaces
71(1)
3.2.8 Modulated Continuous Mappings
72(3)
3.3 Topological Spaces
75(6)
3.3.1 Topological Space Concept
75(1)
3.3.2 Closed Sets, Closure and Interior
76(1)
3.3.3 Convergence in Topological Spaces
77(1)
3.3.4 Continuous Mappings Between Topological Spaces
78(3)
3.4 Convergence Spaces
81(12)
3.4.1 Convergence Space Concept
81(4)
3.4.2 Adherence and Closure
85(1)
3.4.3 Assembling Functions and Assembled Filters
86(1)
3.4.4 Open Sets in a Convergence Space
86(1)
3.4.5 Continuous Mappings Between Convergence Spaces
87(6)
4 Construction of New Spaces
93(28)
4.1 New Spaces via Initial Lifts
93(9)
4.1.1 C-Product Spaces
93(2)
4.1.2 Initial C-Sources
95(2)
4.1.3 Subspaces, Embeddings, and Factorizations
97(1)
4.1.4 Application to Topological Spaces
98(1)
4.1.5 T-Initial Implies C-Initial
99(1)
4.1.6 Fibers of Structures
99(3)
4.2 New Spaces via Final Lifts
102(6)
4.2.1 C-Coproducts
102(1)
4.2.2 Final C-Sinks
103(2)
4.2.3 Quotient Mappings and Factorizations
105(1)
4.2.4 T-Coproducts and Quotients
106(2)
4.3 Topological Reflection of a Convergence Space
108(4)
4.3.1 Topological Convergence Revisited
108(1)
4.3.2 T-Reflection Theorem
109(1)
4.3.3 Reflective Subclasses
110(2)
4.4 Power Spaces
112(5)
4.4.1 Continuous Convergence
112(2)
4.4.2 Cartesian Monoidal Laws
114(1)
4.4.3 Cartesian Exponential Laws
114(3)
4.5 Pseudopowers and Cubes
117(4)
4.5.1 Simple Convergence and Pseudopowers
117(1)
4.5.2 Cubes
117(1)
4.5.3 Uniform Convergence
118(3)
5 Various Kinds of Spaces
121(54)
5.1 Binz Spaces
121(10)
5.1.1 Regular Convergence
122(1)
5.1.2 Hausdorff Convergence
123(1)
5.1.3 Ultrafilters
124(1)
5.1.4 Choquet Space Concept
125(2)
5.1.5 Binz Space Concept
127(1)
5.1.6 Pivot-Embedded C-Space Concept
128(3)
5.2 Tychonoff Spaces
131(4)
5.2.1 Tychonoff Space Concept
131(1)
5.2.2 Zero-Sets and Cozero-Sets
132(1)
5.2.3 Factorization of Tychonoff Mappings
133(2)
5.3 Compactness
135(10)
5.3.1 Compactness Concept
135(1)
5.3.2 Compactness via Coverings
136(1)
5.3.3 Basic Properties of Compact Spaces
137(1)
5.3.4 Continuous Mappings on Compact Domains
138(1)
5.3.5 Compact Spaces and Real Intervals
139(1)
5.3.6 Finite Dimensional Compact Spaces
140(1)
5.3.7 Attainment of Supremum
140(1)
5.3.8 Mapping Spaces with Compact Domain
141(1)
5.3.9 Stone-Weierstrass Approximation
142(3)
5.4 Normality
145(5)
5.4.1 Normal Space Concept
146(1)
5.4.2 Normality Implies Urysohn Separation
146(1)
5.4.3 Urysohn Separation Implies Tietze Extension
147(2)
5.4.4 Tietze Extension Implies Normality
149(1)
5.4.5 Finite Partitions of Unity
149(1)
5.4.6 Normality of Compact Spaces
149(1)
5.5 Local Compactness
150(8)
5.5.1 Locally Compact Concept
150(1)
5.5.2 Compact-Open Topology
151(1)
5.5.3 Compactwise Uniform Convergence
152(1)
5.5.4 Locally Compact Topological Spaces
152(1)
5.5.5 Locally Compact Coreflection
153(1)
5.5.6 Countability and Compactness
154(1)
5.5.7 Compactly Layered Spaces
154(1)
5.5.8 Topological Spaces of Ordinals
155(3)
5.6 Connectedness
158(4)
5.6.1 Connected and Disconnected Spaces
158(1)
5.6.2 Sufficient Conditions
159(1)
5.6.3 Monotonic Homeomorphisms
160(1)
5.6.4 Connected Components
161(1)
5.6.5 Totally Disconnected Spaces
161(1)
5.7 Zero-Dimensional Spaces
162(4)
5.7.1 Zero-Dimensional Space Concept
162(1)
5.7.2 B-Regular Spaces
163(1)
5.7.3 Cantor Representation of the Cube S(N, B)
163(3)
5.8 Baire Spaces
166(2)
5.8.1 Baire Space Concept
166(1)
5.8.2 Compact Spaces Are Baire
167(1)
5.8.3 Locally Compact T-Spaces Are Baire
167(1)
5.8.4 Complete Metric Spaces Are Baire
168(1)
5.9 T0-Spaces
168(7)
5.9.1 T0-Space Concept
169(1)
5.9.2 Front Topology
170(1)
5.9.3 Front Dense Mappings
171(1)
5.9.4 Front Closed Embeddings
171(1)
5.9.5 Sober Spaces
172(3)
6 Fundamentals of Linear Continuity
175(76)
6.1 Gauged Spaces
175(6)
6.1.1 Variable Scalar Field
175(1)
6.1.2 Seminorms
176(1)
6.1.3 Gauged Spaces and Mappings
176(2)
6.1.4 Gauged Spaces via Initial Lifts
178(1)
6.1.5 Gauged Spaces via Final Lifts
179(1)
6.1.6 Gauged Quotient Mappings
179(2)
6.2 Hahn-Banach Extension and Separation
181(7)
6.2.1 Convex Sets and Semiballs
181(2)
6.2.2 Heminorms and Hemiballs
183(1)
6.2.3 Dominated Linear Extensions
184(2)
6.2.4 Convex Separation
186(2)
6.3 Gauged Spaces as Topological Vector Spaces
188(10)
6.3.1 Topological Vector Spaces
188(1)
6.3.2 Continuity Criteria for Seminorms
188(1)
6.3.3 Semiballs and Hubbed Spaces
189(2)
6.3.4 GV-Functionals: Extension and Separation
191(1)
6.3.5 Weakly Gauged Spaces
192(1)
6.3.6 Separated Gauged Spaces
193(1)
6.3.7 Translation-Invariant Metrics
193(2)
6.3.8 Frechet Space Concept
195(2)
6.3.9 Metrizable Inversion Theorem
197(1)
6.4 Normed Spaces Revisited
198(8)
6.4.1 Normed Spaces as TV-Spaces
198(1)
6.4.2 Linear Continuous Mappings Between Normed Spaces
199(1)
6.4.3 Banach Spaces
199(1)
6.4.4 Absolutely Convergent Series
200(1)
6.4.5 Linear Homeomorphism Not Isolated
201(1)
6.4.6 Normed Dual Spaces
202(1)
6.4.7 Normed Bidual Spaces
203(3)
6.5 CV-Spaces and CV-Mappings
206(3)
6.5.1 Convergence Vector Spaces
206(2)
6.5.2 CV-Subspaces
208(1)
6.5.3 CV-Mappings
208(1)
6.5.4 Locally Convex CV-Spaces
208(1)
6.6 Parapowers, Paraduals and Cubes
209(8)
6.6.1 Parapowers C[ X, F] and Cubes S[ J, F]
209(1)
6.6.2 CV-Powers, CV-Duals, and Paraduals
210(2)
6.6.3 Preliminaries About Standard CV Constructions
212(2)
6.6.4 eCV-Space Concept
214(1)
6.6.5 Finite Dimensional CV-Spaces
214(1)
6.6.6 Completeness for CV-Spaces
215(2)
6.7 Equicontinuity and Compactness
217(11)
6.7.1 Equicontinuous Subsets
217(1)
6.7.2 Equicontinuity and Simple Convergence
218(1)
6.7.3 Compact Subspaces of Paraduals
219(1)
6.7.4 Equicontinuous Subsets of Parapowers
219(1)
6.7.5 Bounded Sets in CV-Spaces
220(1)
6.7.6 Which Gauged Spaces Are Locally Compact?
221(1)
6.7.7 CV-Duals of Gauged Spaces
222(1)
6.7.8 Polar Sets in a DGV-Space
222(2)
6.7.9 Representation of Separated and Complete G V-Spaces
224(1)
6.7.10 Extreme Subsets and Extreme Points
225(1)
6.7.11 Krein-Milman Theorem
226(2)
6.8 Riesz-Radon Representation
228(23)
6.8.1 Mosaics
229(1)
6.8.2 Measures
230(1)
6.8.3 Bounded Measures and Jordan Decomposition
231(2)
6.8.4 Radon Measures
233(2)
6.8.5 Radon Integrals
235(2)
6.8.6 Measures via Premeasures
237(1)
6.8.7 Decomposition of M-Valued Linear Functionals
238(2)
6.8.8 Measures Determined by Nonnegative CV-Functionals
240(1)
6.8.9 Measures Determined by CV-Functionals
241(2)
6.8.10 Two Riesz-Radon Representations
243(1)
6.8.11 Approximation by Elementary Functionals
244(7)
7 Basic Categorical Concepts
251(76)
7.1 Categories
251(4)
7.1.1 Category Concept
251(1)
7.1.2 Examples of Categories
252(1)
7.1.3 Subcategories
253(1)
7.1.4 Opposite Categories
254(1)
7.2 Functors
255(5)
7.2.1 Functor Concept
255(2)
7.2.2 Functors Induced by Objects
257(1)
7.2.3 Opposite Functors
258(1)
7.2.4 Bifunctors
259(1)
7.3 Kinds of Arrows
260(7)
7.3.1 Epis
260(1)
7.3.2 Monos
261(1)
7.3.3 Duality Principle
262(1)
7.3.4 Isomorphisms
263(1)
7.3.5 Retractions and Sections
263(2)
7.3.6 Sources and Sinks
265(1)
7.3.7 Epis via Coseparators
265(2)
7.4 Natural Transformations
267(7)
7.4.1 Natural Transformation Concept
267(1)
7.4.2 Algebraic Operations as Natural Transformations
268(1)
7.4.3 Reincarnation Transformation
269(1)
7.4.4 Functors of Several Variables
270(1)
7.4.5 Monoidal Laws in S
270(1)
7.4.6 Evaluation as Natural Transformation
271(1)
7.4.7 Exponential Laws for S
272(2)
7.5 Adjoint Functors
274(13)
7.5.1 Adjoint Functor Concept
274(3)
7.5.2 Adjunctions Associated with S-Powers
277(1)
7.5.3 A Right (and Left) Adjoint Underlying Functor
278(1)
7.5.4 Free Vector Space Functor as Left Adjoint
278(1)
7.5.5 Cube Functor as Right Adjoint
278(1)
7.5.6 Adjoint Functor Properties
279(2)
7.5.7 Reflective Subcategories
281(1)
7.5.8 Coreflective Subcategories
281(1)
7.5.9 Yoneda Lemma
282(1)
7.5.10 Equivalence Functors and Equivalent Categories
283(4)
7.6 Limit Sources
287(14)
7.6.1 Limit Sources for Functors
287(2)
7.6.2 Cartesian Products in S
289(1)
7.6.3 Cartesian Product of Arrows
289(1)
7.6.4 Equalizers as Limit Sources
290(1)
7.6.5 Regular Monos
291(1)
7.6.6 Pullbacks in S
292(1)
7.6.7 Limits for Nonsmall Intersection Functors
293(1)
7.6.8 Well-Powered and Cowell-Powered Categories
294(1)
7.6.9 Limit Source Properties
295(1)
7.6.10 Categorical Completeness Criterion
296(1)
7.6.11 Associated Down-Directed Functors
297(1)
7.6.12 Right Adjoints Preserve Limit Sources
298(1)
7.6.13 Limit Sources That Preserve Monos
299(2)
7.7 Colimit Sinks
301(5)
7.7.1 Colimit Sinks for Functors
301(1)
7.7.2 Coequalizers in S
302(1)
7.7.3 Coproducts in S
303(1)
7.7.4 Pushouts in S
303(1)
7.7.5 Colimit Sink Properties
304(2)
7.8 Concrete Categories and Lifting Categories
306(9)
7.8.1 The Concept Concrete Category
306(1)
7.8.2 Initial Sources and Final Sinks in Concrete Categories
307(1)
7.8.3 Initial Lifts Exist Iff Final Lifts Exist
308(1)
7.8.4 Lifting Categories
309(1)
7.8.5 Lifting Functors Are Right Adjoint
310(1)
7.8.6 Further Lifting Properties
310(1)
7.8.7 Preservation of Initial Monosources
311(1)
7.8.8 Preservation of Final Episinks
312(3)
7.9 Dicomplete Categories
315(4)
7.9.1 Dicompleteness Concept
315(1)
7.9.2 Dicompleteness of Lifting Categories
316(1)
7.9.3 Reflective Subcategories Inherit Dicompleteness
316(2)
7.9.4 Coreflective Subcategories Inherit Dicompleteness
318(1)
7.10 Factorization in Dicomplete Categories
319(8)
7.10.1 Epi-Determined Monos
319(2)
7.10.2 Canonical Factorizations
321(2)
7.10.3 Preservation of Xepi and Dmono
323(1)
7.10.4 The Classes Epi and Dmono in RC
324(3)
8 The Category C
327(10)
8.1 Foundational Categories
327(10)
8.1.1 Foundational Category Concept
327(1)
8.1.2 Cartesian Monoidal Laws
328(2)
8.1.3 Cartesian Exponential Laws
330(1)
8.1.4 Adjunctions Implied by Exponential Laws
331(1)
8.1.5 Extended Exponential Laws
332(1)
8.1.6 Enriched Categories and Functors
332(1)
8.1.7 Enriched Adjunctions and Powered Subcategories
332(5)
9 Reflective Subcategories of C
337(14)
9.1 Tools for Creating Epireflective Subcategories
337(3)
9.1.1 Epireflection Via Adjunction
338(1)
9.1.2 Enriched Epireflection Via Adjunction
339(1)
9.2 Categories of Pivot-Regular Spaces
340(4)
9.2.1 Pivot-Regular Space Concept
340(1)
9.2.2 Pivot-Regular Properties
340(1)
9.2.3 Particular Pivot-Regular Categories
341(1)
9.2.4 Extremal Monosources
342(2)
9.3 Categories of Pivot-Biregular Spaces
344(2)
9.3.1 Pivot-Biregular Spaces
344(1)
9.3.2 Particular Pivot-Biregular Categories
345(1)
9.4 Categories of Pivot-Embedded Spaces
346(5)
9.4.1 Pivot-Embedded Space Concept
346(1)
9.4.2 Properties of PC
347(1)
9.4.3 Epis in Pivot-Embedded Subcategories
347(1)
9.4.4 The Class Dmono(PC)
348(1)
9.4.5 Particular Pivot-Embedded Categories
348(3)
10 Enriched Dualities
351(18)
10.1 Categories of Continuously Algebraic Theory
351(8)
10.1.1 Convergence Vector Space Concept Revisited
352(1)
10.1.2 CV-Mappings
352(1)
10.1.3 CV as Two-fold Concrete Category
353(1)
10.1.4 Creation of Parapowers
354(1)
10.1.5 Convergence Rings and Convergence Algebras
354(2)
10.1.6 Paradual Adjunctions
356(3)
10.2 The Binz Duality
359(7)
10.2.1 Enriched Duality via R
359(3)
10.2.2 Reincarnation Mapping of a Binz Space
362(1)
10.2.3 Enriched Duality via C
363(1)
10.2.4 Convergence Probes
363(2)
10.2.5 Enriched Duality via H
365(1)
10.3 Further Enriched Dualities
366(3)
10.3.1 Enriched Duality via B
366(1)
10.3.2 The Category of Convergence Lattices
366(1)
10.3.3 Enriched Duality via S
367(2)
11 The Category CV
369(24)
11.1 Dicompleteness of CV
369(8)
11.1.1 Limit Sources in CV
369(2)
11.1.2 CV Lifting over V
371(1)
11.1.3 Coequalizers and Quotients in CV
372(1)
11.1.4 Finite Coproducts in CV
373(1)
11.1.5 An Up-Directed Colimit of Finite Products
374(2)
11.1.6 General Coproducts in CV
376(1)
11.1.7 Final Episinks and Colimits
376(1)
11.1.8 CV Is Dicomplete
376(1)
11.2 CV-Powers and Parapowers
377(5)
11.2.1 Parapower Functors into CV
378(1)
11.2.2 CV-Power Functor
378(2)
11.2.3 CV Enriched Adjunctions
380(1)
11.2.4 CV-Enriched Epireflection
380(1)
11.2.5 The CV-Dual Functor
381(1)
11.3 Paratensor Products
382(5)
11.3.1 Paratensor Product Spaces
382(1)
11.3.2 The Paratensor Functor
383(2)
11.3.3 Adjunctions via Paratensors
385(1)
11.3.4 The Free CV-Space Functor
386(1)
11.4 Tensor Products
387(6)
11.4.1 Multilinear Mappings
387(1)
11.4.2 Tensor Product Spaces
388(1)
11.4.3 Tensor Product Functors
389(1)
11.4.4 Tensor Exponential Law
390(1)
11.4.5 Overview of CV as Category
391(2)
12 Reflective Subcategories of CV
393(10)
12.1 Categories of Gauged Spaces
393(1)
12.1.1 GV Rigidly Reflective in CV
393(1)
12.1.2 sGV Quotient Reflective in GV
394(1)
12.2 The Category eCV
394(6)
12.2.1 Characterization of eCV-Space
394(1)
12.2.2 eCV Enriched Epireflective
395(1)
12.2.3 Exponential Laws in eCV
396(1)
12.2.4 Free eCV-Spaces
396(1)
12.2.5 Tensor Products in eCV
397(1)
12.2.6 Initial Lifts over V Exist for Monosources
397(1)
12.2.7 sGV Rigidly Reflective in eCV
398(1)
12.2.8 eCV-Hyperplanes
398(1)
12.2.9 Rmono, Epi, and Dmono in eCV and sGV
399(1)
12.3 The Category oCV
400(3)
12.3.1 oCV-Spaces
400(1)
12.3.2 Exponential Laws in oCV
401(1)
12.3.3 Completeness of oCV-Spaces
401(1)
12.3.4 Free oCV-Spaces
402(1)
13 Linear Continuous Representations
403(14)
13.1 Gauged Reflection of Paraduals
403(5)
13.1.1 Bounded Mappings in Paraduals
403(1)
13.1.2 When the Exponent Space Is Compact
404(1)
13.1.3 The Carrier of a Continuous Seminorm
404(3)
13.1.4 Representation of ACX as a Union
407(1)
13.1.5 Gauged Reflection of a Paradual
408(1)
13.2 Reflexive Spaces
408(9)
13.2.1 Reflexiveness Concept
408(1)
13.2.2 Paraduals Are Reflexive
409(2)
13.2.3 Subspaces That Inherit Reflexiveness
411(1)
13.2.4 cGV Epireflective in sGV and oCV
412(1)
13.2.5 Extended Riesz-Radon Representation
412(5)
14 Smooth Continuity
417(30)
14.1 Averaging Mappings
418(8)
14.1.1 Averaging Mapping Concept
418(1)
14.1.2 AV-Mappings for R-Valued Curves
419(3)
14.1.3 R-Valued Curves and Paths
422(2)
14.1.4 Primary and Active Paths
424(2)
14.2 The Fundamental Isomorphism
426(12)
14.2.1 Spaces of AV-Mappings
426(1)
14.2.2 Join of AV-Mappings
427(2)
14.2.3 Affine and Piecewise Affine Mappings
429(2)
14.2.4 Piecewise Simple AV-Mappings
431(1)
14.2.5 Establishment of the Fundamental Isomorphism
432(1)
14.2.6 E-Valued Curves and Paths
433(1)
14.2.7 Path Spaces
434(4)
14.3 Calculus of Vector-to-Vector Mappings
438(9)
14.3.1 Tangentful Subspaces
438(1)
14.3.2 C1-Mappings on Vector Domains
439(2)
14.3.3 Quasiprimary Mappings
441(1)
14.3.4 Difference Factorizers
442(1)
14.3.5 Vector to Vector Cn-Mappings
443(4)
Supplementary Reading 447(4)
References 451(2)
Index 453
Louis D. Nel is Professor Emeritus of Mathematics at Carleton University. His research interests include topology, category theory, and functional analysis.