COMPARISON OF TOPOLOGIES ON THE FAMILY OF ALL TOPOLOGIES ON X

Abstract

Topology may described a pattern of existence of elements of a given set X. The family (cid:28) (X) of all topologies given on a set X form a complete lattice. We will give some topologies on this lattice (cid:28) (X) using a fixed topology on X and we will regard (cid:28) (X) a topological space. Our purpose of this study is to comparison new topologies on the family (cid:28) (X) of all topologies induced old one.

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