Separation, connectedness, and disconnectedness

Authors: MEHMET BARAN

Abstract: The aim of this paper is to introduce the notions of hereditarily disconnected and totally disconnected objects in a topological category and examine the relationship as well as interrelationships between them. Moreover, we characterize each of $T_{2}$, connected, hereditarily disconnected, and totally disconnected objects in some topological categories and compare our results with the ones in the category of topological spaces.

Keywords: Closure operator, $T _{2}$ spaces, connected spaces, hereditarily disconnected spaces, totally disconnected spaces

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