Topology has its roots in geometry and analysis. From a geometric point of view, topology was the study of properties preserved by a certain group of transformations, namely the homeomorphisms. Certain notions of topology are also abstractions of classical concepts in the study of real or complex functions. These concepts include open sets, continuity, connectedness, compactness, and metric spaces. They were a basic part of analysis before being generalized in topology.

Fuzzy Topological Spaces

This paper gives the first comprehensive account on various systems of axioms of fixed-basis, L-fuzzy topological spaces and their corresponding convergence theory. In general we do not pursue the historical development, but it is our primary aim to present the state of the art of this field. We focus on the following problems:

Axiomatic Foundations Of Fixed-Basis Fuzzy Topology

CONTENTS Introduction ??0. Preliminaries: fuzzy sets ??1. Fuzzy topological spaces: the basic categories of fuzzy topology ??2. Fundamental interrelations between the category Top of topological spaces and the categories of fuzzy topology ??3. Local structure of fuzzy topological spaces ??4. Convergence structures in fuzzy spaces ??5. Separation in fuzzy spaces ??6. Normality and complete regularity type properties in fuzzy topology ??7. Compactness in fuzzy topology ??8. Connectedness in fuzzy spaces ??9. Fuzzy metric spaces and metrization of fuzzy spaces ??10. The fuzzy real line and its subspaces ??11. Fuzzy modification of a linearly ordered space ??12. Fuzzy probabilistic modification of a topological space ??13. The interval fuzzy real line ??14. On hyperspaces of fuzzy sets ??15. Another view of the subject of fuzzy topology and certain categorical aspects of it Conclusion: some reflections on the role and significance of fuzzy topology References

https://iopscience.iop.org/article/10.1070/RM1989v044n06ABEH002295/pdf

Two decades of fuzzy topology: basic ideas, notions, and results

Basic structures of fuzzy topology

A cross-lagged model of self-esteem and life satisfaction: Gender differences among Chinese university students

Fuzzy Hausdorff topological spaces

Relationship between Self-concept and Self-esteem in adolescents

Self-esteem and academic achievement of adolescents.

On fuzzy hausdorffness concepts

In this paper we have studied separation axioms Ti, i = 0, 1, 2 in an intuitionistic fuzzy topological space introduced by Coker. We also show the existence of functors B : IF-Top → BF-Top and D : BF-Top → IF-Top and observe that D is left adjoint to B.

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Rekha Srivastava

Papers

Fuzzy Hausdorff topological spaces

Relationship between Self-concept and Self-esteem in adolescents

Self-esteem and academic achievement of adolescents.

On fuzzy hausdorffness concepts

Separation axioms in intuitionistic fuzzy topological spaces