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Home 2020

Separation Axioms Weaker Than T1

Authors: Khadiga Ali Arwini, Mabrouka Mohammed Almrgni, 144 (2020) 158-168

2024-01-13
Reading Time: 2 mins read
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ABSTRACT

The purpose of this paper is to introduce a new type of separation axioms via dense sets, called DTi-spaces (i = 0‚1 4 ‚1 3 ‚1 2‚3 4‚1), where a DTi-space is a topological space which contains a dense Ti-subspace (i = 0‚1 4 ‚1 3 ‚ 1 2 ‚3 4‚1). These new axioms are weaker than the axiom of T1. We provide the basic properties of DTi- spaces (i = 0‚1 4‚1 3 ‚1 2 ‚3 4‚1), and we show that the axioms of DT1 4, DT13, DT12, DT34, DT1 are open hereditary. Moreover, we study the connections between these axioms and the axioms of Ti where (i = 0‚1 4 ‚1 3 ‚1 2 ‚3 4‚1).

 

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Tags: lower separation axiomsproduct spacessubspaces
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