T₁ Approach Spaces

Abstract

In this paper, we characterize both T 1 and local T 1 limit (resp. gauge) approach spaces as well as show how these concepts are related to each other. Finally, we compare these T 1 and the usual T 1 approach spaces.

The Fell approach structure

“…□ Remark 1. In [7] and [8] Baran and Qasim gave different definitions of T 0 and T 1 approach spaces. We hope that the characterization given in Proposition 1 will lead a way to give an analogue definition of T 2 spaces (Hausdorff spaces).…”

The notions of closedness and D-connectedness in quantale-valued approach spaces

“…Let L be a value quantale, and let (X, B) be an L-approach space and p ∈ X. Then, the following are equivalent: , then local T 0 (respectively, local T 1 ) L-approach spaces are reduced to classical local T 0 (respectively, local T 1 ) approach spaces defined in [12,13]. A) is an L-approach distance space.…”