Hausdorff objects

Abstract

In previous papers, several extensions of the $T_{2}$ separation property in topology to a topological category were compared. The aim of this paper is to develop further results relating to these extensions as well as to solve several open problems. Moreover, we show one of these $T_{2}$, namely $KT_{2}$ limit spaces and reciprocal limit spaces are equivalent and every $KT_{2}$ limit space induces the associated complete uniform limit space. Finally, we compare our results and give some applications.

Keywords

• $T_{2}$ objects
• reciprocal limit spaces
• uniform limit spaces
• sober spaces
• pre-Hausdorff objects

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