Some results on smooth fuzzy subspaces and Hausdorff spaces

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.