Abstract
In this article, by using the notion of chain, we give some characterizations of totally separated spaces. Then, we give some examples, study the properties of those spaces and give new proofs. Furthermore, by using the notion of chain, we introduce the notions of totally weakly chain separated and totally chain separated sets in a topological space, we state some useful aspects of these sets as well as the various relationships between them and by using these notions we give some characterizations of discrete and totally separated spaces.
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