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Separation, Connectedness, And Disconnectedness, Mehmet Baran
Separation, Connectedness, And Disconnectedness, Mehmet Baran
Turkish Journal of Mathematics
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.