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$T4$ space (Definition)
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.

Notes

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.

Bibliography

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.



"$T4$ space" is owned by matte.
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See Also: separation axioms, How are normal and T4 spaces defined in books?
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Cross-references: normal, separation axioms, open sets, closed sets, disjoint, topological space
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This is version 2 of $T4$ space, born on 2004-10-08, modified 2004-10-08.
Object id is 6318, canonical name is T4Space.
Accessed 1278 times total.

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AMS MSC: 54D15 (General topology :: Fairly general properties :: Higher separation axioms )
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