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.
Author(s): Anjaly Jose, Sunil C. Mathew
Publisher: Springer
Year: 2022
Language: English
Pages: 101
City: Singapore
Preface
Chapters Description
Acknowledgement
Contents
About the Authors
1 Motivation and Preliminaries
1.1 Introduction
1.2 Fuzzy Topological Spaces
1.3 upper LL-Topological Spaces
References
2 H-Fuzzy Topological Spaces
2.1 H-Fuzzy Topological Spaces
2.2 H-Fuzzy Topologies of Degree nn
2.3 Exercises
References
3 Invertible Fuzzy Topological Spaces
3.1 Invertibility of Fuzzy Topological Spaces
3.2 Completely Invertible Fuzzy Topological Spaces
3.3 Homogeneity and Invertibility
3.4 Orbits in Invertible Fuzzy Topological Spaces
3.5 Exercises
References
4 Types of Invertible Fuzzy Topological Spaces
4.1 Inverting Pairs
4.2 Type 1 and Type 2 Invertible Fuzzy Topological Spaces
4.3 Exercises
Reference
5 Properties of Invertible Fuzzy Topological Spaces
5.1 Separation and Invertibility
5.2 Countability and Invertibility
5.3 Compactness and Invertibility
5.4 Connectedness and Invertibility
5.5 Exercises
References
6 Invertibility of the Related Spaces
6.1 Sums and Subspaces
6.2 Simple Extensions
6.3 Associated Spaces
6.4 Quotient Spaces
6.5 Product Spaces
6.6 Exercises
References
7 Invertible upper LL-Topological Spaces
7.1 Invertibility in upper LL-Topologies
7.2 Completely Invertible upper LL-Topological Spaces
7.3 Types of Invertible upper LL-Topologies
7.4 Local to Global Properties of Invertible upper LL-Topologies
7.5 Exercises
References
Appendix Index
Index
