On topological properties of the Hausdorff fuzzy metric spaces

Abstract

In the paper, necessary and sufficient conditions for two Hausdorff fuzzy metric spaces to be homeomorphic are studied. Also, several properties of the Hausdorff fuzzy metric spaces, as Fboundedness, separability and connectedness are explored.

Himpunan Kompak Pada Ruang Metrik Fuzzy

“…Definisi 2.4. [6] Misalkan X adalah suatu himpunan tak kosong, * adalah suatu norm-t kontinu, dan M adalah suatu himpunan fuzzy pada X ×X ×(0, ∞). (X, M, * ) dikatakan suatu ruang metrik fuzzy apabila untuk setiap x, y, z ∈ X dan s, t ∈ (0, ∞) berlaku kondisi berikut:…”

The depth and the attracting centre for a continuous map on a fuzzy metric interval

“…In order to obtain a Hausdorff topology in fuzzy metric spaces, George and Veeramani [1] modified the notion given by Kramosil and Michalek in a slight but appealing way. Recently many authors studied several properties of the Hausdorff fuzzy metric spaces (see [6,8,11]) and introduced and investigated the different types of fuzzy contractive maps and obtained a lot of fixed point theorems (see [3,4,9,10,13,14,15,16]). Until now, there are little of works that investigates some properties of discrete dynamical systems on fuzzy metric spaces.…”