Wilansky presents this mathematics text for advanced undergraduates and beginning graduate students on the subject of topological vector spaces. Chapter 1 presents basic foundations and definitions of set theory, computation, vector spaces, and topology. Next covered are metrics, Banach space, construction of topological vector spaces, map and graph theorems, local convexity, and an assortment of additional topics deemed necessary to proceed to chapter 8, which addresses duality. The remainder of the book proceeds from this theme, discussing equicontinuity, the strong topology, operators, completeness, inductive limits, compactness, and barrelled spaces. An appendix of tables summarizes theorems treated. The text is written in technical mathematical style, consisting mostly of proofs with clearly labeled lemmas, corollaries, examples, remarks, and practice problems. Annotation ©2014 Book News, Inc., Portland, OR (booknews.com)
Geared toward beginning graduate students of mathematics, this text covers Banach space, open mapping and closed graph theorems, local convexity, duality, equicontinuity, operators, inductive limits, and compactness and barrelled spaces. 1978 edition.
