Journal of the Chungcheong Mathematical Society (충청수학회지)

The Chungcheong Mathematical Society (충청수학회)
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THETA TOPOLOGY AND ITS APPLICATION TO THE FAMILY OF ALL TOPOLOGIES ON X

  • Received : 2015.04.29
  • Accepted : 2015.07.22
  • Published : 2015.08.15
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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 topology on X and regard ${\tau}(X)$ a topological space. Our purpose of this study is to give new topologies on the family ${\tau}(X)$ of all topologies induced by old one and its ${\theta}$ topology and to compare them.

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References

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  1. COMPARISON OF TOPOLOGIES ON THE FAMILY OF ALL TOPOLOGIES ON X vol.31, pp.4, 2015, https://doi.org/10.14403/jcms.2018.31.1.387