Lindelöf T3 Space is Paracompact

Theorem

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

Then $T$ is paracompact.

Proof

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Sources

• 1978: Lynn Arthur Steen and J. Arthur Seebach, Jr.: Counterexamples in Topology (2nd ed.) ... (previous) ... (next): Part $\text I$: Basic Definitions: Section $3$: Compactness: Compactness Properties and the $T_i$ Axioms