$T4$ 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.
随便看	subnormal subgroup SubquiverAndImageOfAQuiver subquiver and image of a quiver SubRiemannianManifold Sub-Riemannian manifold Subring subring Subsemiautomaton subsemiautomaton SubsemigroupOfACyclicSemigroup subsemigroup of a cyclic semigroup SubsemigroupSubmonoidAndSubgroup subsemigroup,, submonoid,, and subgroup Subsequence subsequence Subset subset SubsetConstruction subset construction Subsets and propositional resizing SubsetsOfCountableSetsAreCountable subsets of countable sets are countable SubsheafOfAbelianGroups subsheaf of abelian groups SubspaceOfASubspace

T⁢4 space

Definition 1.

Notes

References

$T4$ space