On Extensions of Topologies
1967 ◽
Vol 19
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pp. 474-487
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Keyword(s):
If (X, τ) is a topological space (with topology τ) and A is a subset of X, then the topology τ(A) = {U ⋃ (V ⋂ A)|U, V ∈ τ} is said to be a simple extension of τ. It seems that N. Levine introduced this concept in (4) and he proved, among other results, the following:(A) If (X, τ) is a regular (completely regular) space and A is a closed subset of X, then (X, τ(A)) is a regular (completely regular) space.(B) Let (X, τ) be a normal space, and A a closed subset of X. Then (X, τ(A)) is normal if and only if X — A is a normal subspace of (X, τ).(C) Let (X, τ) be a countably compact (compact or Lindelöf) and A ∉ τ.
1975 ◽
Vol 19
(3)
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pp. 221-229
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Keyword(s):
2017 ◽
Vol 20
(10)
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pp. 68-73
Keyword(s):
1984 ◽
Vol 36
(1)
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pp. 38-57
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Keyword(s):
Keyword(s):
1970 ◽
Vol 22
(6)
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pp. 1208-1210
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Keyword(s):
1999 ◽
Vol 42
(3)
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pp. 291-297
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Keyword(s):
2015 ◽
Vol 26
(03)
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pp. 1550032
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Keyword(s):