Quasi-homeomorphisms and lattice-equivalences of topological spaces
1972 ◽
Vol 14
(1)
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pp. 41-44
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Keyword(s):
In his paper [1], Thron introduced a concept of lattice-equivalence of topological spaces. Let C(X) denote the lattice of all closed sets of a topological space X. Two topological spaces X and Y are said to be lattice-equivalent if there exists a lattice-isomorphism between C(X) and C(Y). It is clear that for any continuous function f: X → Y, the induced map ψf: C(Y) → C(X), defined by ψ(F)=f−1(F), is a lattice-homomorphism. Furthermore, if h: X→ Y is a homeomorphism then ψh: C(Y) → C(X) is a lattice-isomorphism. Thron proved among others that for TD-spaces X and Y, any lattice-isomorphism: C(Y) → C(X) can be induced by a homeomorphism f: X → Y in the above way.
2020 ◽
Vol 9
(3)
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pp. 1306-1313
2016 ◽
Vol 4
(2)
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pp. 151-159
2012 ◽
Vol 20
(1)
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pp. 307-316
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