COMPARISON OF TOPOLOGIES ON THE FAMILY OF ALL TOPOLOGIES ON X

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

Abstract

1. Introduction

2. Topology on the family 𝜏(X) related to the 𝜃 topologies on X

3. Topology on the family 𝜏(X) related to the 𝜃 topologies on X

4. Topology on the family 𝜏(X) related to the semi-regular topology on X

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