Open AccessWeakly chain separated sets in a topological space
Author(s) -
Nikita Shekutkovski,
Zoran Misajleski,
Aneta Velkoska,
Emin Durmishi
Publication year - 2021
Publication title -
mathematica montisnigri
Language(s) - English
Resource type - Journals
eISSN - 2704-4963
pISSN - 0354-2238
DOI - 10.20948/mathmontis-2021-52-1
Subject(s) - chain (unit) , topological space , mathematics , space (punctuation) , topology (electrical circuits) , social connectedness , connected space , zero dimensional space , combinatorics , pure mathematics , topological vector space , physics , computer science , psychology , astronomy , psychotherapist , operating system
In this paper we introduce the notion of pair of weakly chain separated sets in a topological space. If two sets are chain separated in the topological space, then they are weakly chain separated in the same space. We give an example of weakly chain separated sets in a topological space that are not chain separated in the space. Then we study the properties of these sets. Also we mention the criteria for two kind of topological spaces by using the notion of chain. The topological space is totally separated if and only if any two different singletons (unit subsets) are weakly chain separated in the space, and it is the discrete if and only if any pair of different nonempty subsets are chain separated. Moreover we give a criterion for chain connected set in a topological space by using the notion of weakly chain separateness. This criterion seems to be better than the criterion of chain connectedness by using the notion of pair of chain separated sets. Then we prove the properties of chain connected, and as a consequence of connected sets in a topological space by using the notion of weakly chain separateness.