T3 Lindelöf Space is T4 Space/Proof 2

Theorem

Let $T = \struct {S, \tau}$ be a $T_3$ Lindelöf topological space.

Then:

$T$ is a $T_4$ space.

Proof

From $T_3$ Lindelöf Space is Fully $T_4$ Space:

$T$ is a fully $T_4$ space.

From Fully $T_4$ Space is $T_4$ Space:

$T$ is a $T_4$ space.

$\blacksquare$