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A note on closedness and connectedness in the category of proximity spaces

Kula Muammer (Erciyes University, Department of Mathematics, Kayseri, Turkey)
Maraşlı Tuğba (Erciyes University, Department of Mathematics, Kayseri, Turkey)
Özkan Samed (Erciyes University, Department of Mathematics, Kayseri, Turkey)

In this paper, an explicit characterization of the separation properties T0 and T1 at a point p is given in the topological category of proximity spaces. Furthermore, the (strongly) closed and (strongly) open subobjects of an object are characterized in the category of proximity spaces and also the characterization of each of the various notions of the connected objects in this category are given.

Keywords: topological category, proximity space, separation, closedness, connectedness