This book discusses the invertibility of fuzzy topological spaces and related topics. Certain types of fuzzy topological spaces are introduced, and interrelations between them are brought forth. Various properties of invertible fuzzy topological spaces are presented, and characterizations for completely invertible fuzzy topological spaces are discussed. The relationship between homogeneity and invertibility is examined, and, subsequently, the orbits in an invertible fuzzy topological space are studied. The structure of invertible fuzzy topological spaces is investigated, and a clear picture of the inverting pairs in an invertible fuzzy topological space is introduced. Further, the related spaces such as sums, subspaces, simple extensions, quotient spaces, and product spaces of invertible fuzzy topological spaces are examined. In addition, the effect of invertibility on fuzzy topological properties like separation axioms, axioms of countability, compactness, and fuzzy connectedness in invertible fuzzy topological spaces is established. The book sketches ideas extended to the bigger canvas of L-topology in a very interesting manner.
Arvustused
The book is well written, provides most of its required preliminaries and will be of interest to all the researchers (or even experienced undergraduates) studying fuzzy or lattice-valued topology. (Sergejs Solovjovs, zbMATH 1504.54010, 2023)
Motivation and Preliminaries.- H-fuzzy topological spaces.- Invertible
fuzzy topological spaces.- Types of invertible fuzzy topological spaces.-
Properties of invertible fuzzy topological spaces.- Invertibility of the
related spaces.- Invertible R-topological spaces.
Anjaly Jose is Assistant Professor at the Department of Mathematics, St. Josephs College Devagiri, Calicut, Kerala, India. She is a research guide under the University of Calicut, Kerala. Awarded the doctoral degree from Mahatma Gandhi University Kottayam in 2013, she is a Resource Person and has a number of research publications to her credit. Her areas of interest include topology and fuzzy topology.
Sunil C. Mathew is Principal of Deva Matha College Kuravilangad, Kerala, India. He has more than 26 years of teaching experience at St. Thomas College Palai, Kerala, India. Awarded the doctoral degree in 2003 from Mahatma Gandhi University Kottayam, Kerala, he is a Research Guide of the same university. A resource person with more than 40 international publications to his credit, his interests chiefly lie in fuzzy topology and graph labeling.
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