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COMPARISON OF TOPOLOGIES ON THE FAMILY OF ALL TOPOLOGIES ON X

  • Kim, Jae-Ryong (Department of Information Security, Cryptology, and Mathematics Kookmin University)
  • Received : 2017.10.10
  • Accepted : 2017.09.19
  • Published : 2018.11.15

Abstract

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

Keywords

References

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