PlanetMath: fully T4

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fully T4

(Definition)

A topological space is said to be fully normal if it is a space and is fully .

For example, every pseudometric space is fully .

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.

"fully T4" is owned by Mathprof.

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Also defines:

fully normal

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Cross-references: regular, uniformizable, paracompact, Lindelöf, implications, pseudometric space, star refinement, open cover, topological space
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This is version 4 of fully T4, born on 2007-05-26, modified 2007-05-27.
Object id is 9473, canonical name is FullyT4.
Accessed 775 times total.

Classification:

54D15 (General topology :: Fairly general properties :: Higher separation axioms )

Pending Errata and Addenda

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