The ditopology generated by pre-open and pre-closed sets, and submaximality in textures

Abstract

The authors consider the ditopology generated by pre-open and pre-closed sets and investigate submaximality in ditopological texture spaces.

On some dicardinal functions in ditopological texture spaces

“…The following definitions and propositions were introduced in [1][2][3][4][5][6][7][8][9]15]. A texturing on a non-empty set S is a set S containing S; ; of subsets of S with respect to inclusion satisfying the conditions: .i/ .S; Â/ is a complete lattice .i i / S is completely distributive, .i i i/ S separates the points of S, .iv/ Meets V and finite joins W coincide with intersections T and unions S , respectively.…”

On the position of abstract density topologies in the lattice of all topologies

“…In [6] there was introduced the notion of semi-open sets with respect to some ideal I (so called semi-I-open) and studied the properties of these sets. The research was continued in [15].…”