ST2, ∆T2, ST3, ∆T3, Tychonoff, compact and ∂-connected objects in the category of proximity spaces

Abstract

Inthispaper,anexplicitcharacterizationoftheseparationproperties ST2,∆T2, ST3,∆T3 and Tychonoff objects are given in the topological category of proximity space. Furthermore, the (strongly) compact object and ∂-connected object are also characterized in the category of proximity space. Moreover, we investigate the relationships among ST2, ∆T2, ST3, ∆T3, the separation properties at a point p, the generalized separation properties Ti, i = 0,1,2, T0, T1, T2 and Tychonoff objects in this category. Finally, we investigate the relationships between ∂-connected object and (strongly) connected object in the topological category of proximity space.Mathematics Subject Classification (2010). 54B30, 54D10, 54A05, 54E05, 18B99, 18D15