# $T4$ space

###### 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.

## 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.
Title $T4$ space T4Space 2013-03-22 14:42:15 2013-03-22 14:42:15 matte (1858) matte (1858) 5 matte (1858) Definition msc 54D15 SeparationAxioms HowIsNormalityAndT4DefinedInBooks