$T4$ space

Definition 1.

[1]Suppose $X$ is a topological space. Further, suppose thatfor any two disjointclosed 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 saythat $X$ is a $T_{4}$ space.

Notes

It should be pointed out that there is no standard conventionfor 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.

References

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.

单词	T4Space
释义	$T4$ space Definition 1. [1]Suppose $X$ is a topological space. Further, suppose thatfor any two disjointclosed 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 saythat $X$ is a $T_{4}$ space. Notes It should be pointed out that there is no standard conventionfor 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. References 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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T⁢4 space

Definition 1.

Notes

References

$T4$ space