Fuzzy Semi-Metric Spaces

Abstract

The T 1-spaces induced by the fuzzy semi-metric spaces endowed with the special kind of triangle inequality are investigated in this paper. The limits in fuzzy semi-metric spaces are also studied to demonstrate the consistency of limit concepts in the induced topologies.

Convergence in Fuzzy Semi-Metric Spaces

“…The following results are from Wu [7]. Especially, Part (ii) is modified from Wu [7] by using the similar argument. Proposition 2.…”

“…Gregori and Romaguera [4] proposed the fuzzy quasi-metric spaces in which the symmetric condition was not assumed. Wu [7] studied the so-called fuzzy semi-metric space without assuming the symmetric condition in which four forms of triangle inequalities are considered. The common coincidence points and common fixed points in fuzzy semi-metric spaces were also studied in Wu [8].…”

“…In order to consider the triangle inequalities, we need to introduce the concept of the t-norm. We say that the function * : Since the symmetric condition is not assumed to be true in fuzzy semi-metric space, four kinds of triangle inequalities proposed by Wu [7] are shown below. Definition 2.…”

“…The following results are modified from Wu [7] by using a similar argument, which will be used in the further discussion. Proposition 1.…”

“…From Proposition 2, if M is left-continuous or symmetrically left-continuous with respect to the distance on (0, ∞), or right-continuous and or symmetrically right-continuous with respect to the distance on (0, ∞], then we can just consider the -triangle inequality. The following results are modified from Wu [7] by using a similar argument.…”