On minimal sets and strictly weaker topologies

Abstract

In [1,2] Farrag characterized the stirictly weaker principal topologies than any given principal topology on a nonempty set by using the minimal open sets which are defined by Steiner [3]. This paper mainly generalizes this result by using the minimal sets, which are defined in the paper with respect to the given topology τ on a nonempty set.

Keywords

• Ultratopologies
• Principal and nonprincipal topologies
• Minimal open sets
• T0
• T1
• Regular topologies