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

$\blacksquare$