Some results on smooth fuzzy subspaces and Hausdorff spaces

Murugesan Shakthiganesan 1 *

doi:10.26637/MJM0703/0031

Some results on smooth fuzzy subspaces and Hausdorff spaces

Authors :

Murugesan Shakthiganesan ^{1 *}

Author Address :

¹Department of Applied Mathematics and Computational Sciences, PSG College of Technology, Coimbatore-641004 , India.

Abstract :

In this work, first we prove some interesting results in the context of smooth fuzzy subspaces through bases. In follow, we define the concept of $(\alpha,\ell)$-Hausdorff spaces and prove that the intersection of finitely many $(\alpha,\ell)$-Hausdorff topologies is again an $(\alpha,\ell)$-Hausdorff topology in contrast with the crisp theory; we also prove that product of finitely many $(\alpha,\ell)$-Hausdorff spaces is $(\alpha,\ell)$-Hausdorff. Finally, we define and discuss the concept of $\ell$-Hausdorffness of space.

Keywords :

Smooth fuzzy topological spaces, Subspaces, Hausdorffness.

DOI :

10.26637/MJM0703/0031

Article Info :

Received : September 20, 2016; Accepted : August 08, 2019.