A Critical Study On Fuzzy Hausdorff Space And Its Impact On Topology

Author(s)	Dr. Satish Raj
Country	India
Abstract	Our main aim is to define the relation between the fuzzy set and topological spaces. However the fuzzy sets hypothesis goes in a developing phase, now a days it is accepted spacious and precious applications. We also develop the generalised structure which includes several fields such as point set topology, algebraic topology, and differential topology. Georg Cantor, David Hilbert, Felix Hausdorff, Maurice Frechet and Henri Poincare studied its basic properties based on Euclidean space and some geometrical structure. For that purpose, we have tried to offer more fundamental description of these two topics. In the fuzzy topological spaces section. We derive definition and also proved of theorems. The existing consequences in this analysis signify that large numbers of the fundamental concepts from general topology might be expanded enthusiastically to fuzzy topological spaces.
Keywords	Algebraic Topology, Euclidean space, Fuzzy set, Fuzzy Topology and Hausdorff space.
Field	Mathematics
Published In	Volume 16, Issue 2, April-June 2025
Published On	2025-05-19
DOI	https://doi.org/10.71097/IJSAT.v16.i2.5271

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