T3 Lindelöf Space is Fully T4 Space
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Theorem
Let $T = \struct {S, \tau}$ be a $T_3$ Lindelöf topological space.
Then:
- $T$ is a fully $T_4$ space
Proof
From Lindelöf T3 Space is Paracompact:
- $T$ is a paracompact space
From T3 Space is Fully T4 iff Paracompact:
- $T$ is a fully $T_4$ space
$\blacksquare$