Mathematica Bohemica, Vol. 145, No. 2, pp. 177-190, 2020
$T_2$ and $T_3$ objects at $p$ in the category of proximity spaces
Muammer Kula, Samed Özkan
Received December 27, 2017. Published online June 12, 2019.
Abstract: In previous papers, various notions of pre-Hausdorff, Hausdorff and regular objects at a point $p$ in a topological category were introduced and compared. The main objective of this paper is to characterize each of these notions of pre-Hausdorff, Hausdorff and regular objects locally in the category of proximity spaces. Furthermore, the relationships that arise among the various ${\rm Pre}T_2$, $T_i$, $i=0,1,2,3$, structures at a point $p$ are investigated. Finally, we examine the relationships between the generalized separation properties and the separation properties at a point $p$ in this category.
Keywords: topological category; proximity space; Hausdorff space; regular space
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