δ-connectedness modulo an ideal

Abstract

The aim of this paper is to introduce the notion of δ-connectedness modulo an ideal in proximity spaces. A sufficient condition for a δ-connected modulo an ideal proximity space to be connected modulo an ideal is defined. The notion of δ-connectedness modulo a proximal property is defined, and several results for δ-connectedness modulo compactness and modulo pseudocompactness are obtained. δ-perfect map for proximity spaces is defined and it is shown that the class of δ-perfect maps is properly contained in the class of perfect maps, and some results about δ-perfect maps are substantiated.

Keywords

• δ-connected
• δ-continuous map
• ideal
• smirnov compactification
• proximal property