ST2, delta-T2, ST3, delta-T3, Tychono, compact and lambda-connected objects in the category of proximity spaces

Abstract

In this paper, an explicit characterization of the separation properties 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.