fully T4

A topological space $X$ is said to be fully $T_{4}$ if every open cover of $X$ has star refinement.

A topological space is said to be fully normal if it is a $T_{1}$ space andis fully $T_{4}$ .

For example, every pseudometric space is fully $T_{4}$ .

We have the following implications:

Lindelöf $T_{3}\\Rightarrow$ paracompact and $T_{3}\\Rightarrow$ fully $T_{4}\\Rightarrow T_{4}\\Rightarrow$ uniformizable $\\Rightarrow T_{3}$ ,

and

fully normal $\\Leftrightarrow$ paracompact regular.

单词	FullyT4
释义	fully T4 A topological space $X$ is said to be fully $T_{4}$ if every open cover of $X$ has star refinement. A topological space is said to be fully normal if it is a $T_{1}$ space andis fully $T_{4}$ . For example, every pseudometric space is fully $T_{4}$ . We have the following implications: Lindelöf $T_{3}\\Rightarrow$ paracompact and $T_{3}\\Rightarrow$ fully $T_{4}\\Rightarrow T_{4}\\Rightarrow$ uniformizable $\\Rightarrow T_{3}$ , and fully normal $\\Leftrightarrow$ paracompact regular.
随便看	Leonardo da Pisa LeopoldKronecker Leopold Kronecker LeopoldtsConjecture Leopoldt’s conjecture LeraySpectralSequenceForAnAffineMorphism Leray spectral sequence for an affine morphism LevelCurve level curve LevelSet level set LevelSetsOfSmoothFunctionsOnManifolds level sets of smooth functions on manifolds LeviCivitaConnection Levi-Civita connection LeviCivitaPermutationSymbol Levi-Civita permutation symbol LeviFlat Levi flat LevinReduction Levin reduction LeviPseudoconvex Levi pseudoconvex LevisTheorem Levi’s theorem