$\delta$-connectedness modulo an ideal

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