Partition axioms and lattice - equivalence of topological spaces
The purpose of this paper is to introduce new space structures Do1, Dv1/2and D1 which we shall refer to as partition axioms and prove that two Do-spaces are lattice-equivalent if and only if their T0 identifications are homeomorphic. As a consequence, we have that every cardinal preserving lattice-e...
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| Main Authors: | , |
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| 格式: | Article |
| 语言: | English |
| 出版: |
Faculty of Science, University of Malaya
1975
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| 在线阅读: | http://psasir.upm.edu.my/id/eprint/39854/1/Partition%20axioms%20and%20lattice%20-%20equivalence%20of%20topological%20spaces.pdf http://psasir.upm.edu.my/id/eprint/39854/ |
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| 总结: | The purpose of this paper is to introduce new space structures Do1, Dv1/2and D1 which we shall refer to as partition axioms and prove that two Do-spaces are lattice-equivalent if and only if their T0 identifications are homeomorphic. As a consequence, we have that every cardinal preserving lattice-equivalence between two D1/2 -spaces are induced by a homeomorphism, and a result of Thron (1962) saying that two TD-spaces are lattice-equivalent if they are homeomorphic also follows. |
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