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 space
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(Definition)
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Definition 1 [1] Suppose $X$ is a topological space. Further, suppose that for any two disjoint closed sets $A,B\subseteq X$ , there are two disjoint open sets $U$ and $V$ such that $A\subseteq U$ and $B\subseteq V$ . Then we say that $X$ is a $T_4$ space.
It should be pointed out that there is no standard convention for separation axioms in topology. The above definition follows [1]. However, in some references (e.g. [2]) the meaning of $T_4$ and normal are exchanged.
- 1
- L.A. Steen, J.A.Seebach, Jr., Counterexamples in topology, Holt, Rinehart and Winston, Inc., 1970.
- 2
- J.L. Kelley, General Topology, D. van Nostrand Company, Inc., 1955.
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" space" is owned by matte.
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Cross-references: normal, references, separation axioms, open sets, closed sets, disjoint, topological space
There is 1 reference to this entry.
This is version 2 of  space, born on 2004-10-08, modified 2004-10-08.
Object id is 6318, canonical name is T4Space.
Accessed 1709 times total.
Classification:
| AMS MSC: | 54D15 (General topology :: Fairly general properties :: Higher separation axioms ) |
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Pending Errata and Addenda
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