학술저널
THETA TOPOLOGY AND ITS APPLICATION TO THE FAMILY OF ALL TOPOLOGIES ON X
- 충청수학회
- Journal of the Chungcheong Mathematical Society
- Volume 28, No. 3
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2015.08431 - 441 (11 pages)
- 2
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 topology on X and regard τ (X) a topological space. Our purpose of this study is to give new topologies on the family τ (X) of all topologies induced by old one and its θ topology and to compare them.
1. Introduction
2. Compare of θ topologies defined different topologies
3. Topologies on the family τ (X) induced from by a given topology τ
4. Topology on the family τ (X) related to the θ topologies on X
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