$T4$ space
Definition 1.
[1] Suppose $X$ is a topological space^{}. Further, suppose that for any two disjoint closed sets^{} $A\mathrm{,}B\mathrm{\subseteq}X$, there are two disjoint open sets $U$ and $V$ such that $A\mathrm{\subseteq}U$ and $B\mathrm{\subseteq}V$. Then we say that $X$ is a ${T}_{\mathrm{4}}$ 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 |
---|---|
Canonical name | T4Space |
Date of creation | 2013-03-22 14:42:15 |
Last modified on | 2013-03-22 14:42:15 |
Owner | matte (1858) |
Last modified by | matte (1858) |
Numerical id | 5 |
Author | matte (1858) |
Entry type | Definition |
Classification | msc 54D15 |
Related topic | SeparationAxioms |
Related topic | HowIsNormalityAndT4DefinedInBooks |