Hereditary properties of semi-separation axioms and their applications

Abstract

The paper studies the open-hereditary property of semi-separation axioms and applies it to the study of digital topological spaces such as an n-dimensional Khalimsky topological space, a Marcus-Wyse topological space and so on. More precisely, we study various properties of digital topological spaces related to low-level and semi-separation axioms such as T 1 2 , semi-T 1 2 , semi-T 1 , semi-T 2 , etc. Besides, using the finite or the infinite product property of the semi-T i-separation axiom, i ∈ {1, 2}, we prove that the n-dimensional Khalimsky topological space is a semi-T 2-space. After showing that not every subspace of the digital topological spaces satisfies the semi-T i-separation axiom, i ∈ {1, 2}, we prove that the semi-T iseparation property is open-hereditary, i ∈ {1, 2}. All spaces in the paper are assumed to be nonempty and connected.

Functionally Separation Axioms on General Topology

“…Another generalization of separation axioms was given using functions in the category of topological spaces (see [12]). We draw attention to some separation axioms have been very useful in the study of certain objects in digital topology (see [13,14]). is work is organized as follows: after this introduction, we recall some definitions and results which are required to make this work self-contained.…”

Some Applications of Supra Preopen Sets

“…It should be noted that the supra topological frame can be more convenient to solve some practical problems and to model some phenomena as pointed out in [17]. Also, the possibility of applying semiopen sets to deal with some problems on digital topology has been demonstrated in [18]. e layout of the paper is as follows.…”