Unification approach to the separation axioms between T₀ and completely Hausdorff

1998/10/12 by Francisco G. Arenas, F. G. Arenas, Julian Dontchev +5
Computer Science · Decision Sciences · Mathematics · #54A05 #54D10 #54D30 #54H05 #Advanced Algebra and Logic #Advanced Topology and Set Theory #FOS: Mathematics #Fuzzy and Soft Set Theory #General Topology (math.GN) #math.GN #msc:54A05 #msc:54D10 #msc:54D30 #msc:54H05

paper · pdf · doi:10.48550/arxiv.math/9810074

11 pages

arxiv created 1998/10/12 · openalex publication_date 1998/10/12 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The aim of this paper is to introduce a new weak separation axiom that generalizes the separation properties between T₁ and completely Hausdorff. We call a topological space (X,τ) a T_κ,ξ-space if every compact subset of X with cardinality ≤ κ is ξ-closed, where ξ is a general closure operator. We concentrate our attention mostly on two new concepts: kd-spaces and T_1/3-spaces.

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