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$T_{2}$ and $T_{3}$ objects at $p$ in the category of proximity spaces
Mathematica Bohemica, Tome 145 (2020) no. 2, pp. 177-190 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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.
DOI : 10.21136/MB.2019.0144-17
Classification : 18B99, 54B30, 54D10, 54E05
Keywords: topological category; proximity space; Hausdorff space; regular space 
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Kula, Muammer; Özkan, Samed. $T_{2}$ and $T_{3}$ objects at $p$ in the category of proximity spaces. Mathematica Bohemica, Tome 145 (2020) no. 2, pp. 177-190. doi: 10.21136/MB.2019.0144-17

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