Countable Discrete Space is Lindelöf
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Theorem
Let $T = \struct {S, \tau}$ be a countable discrete topological space.
Then $T$ is a Lindelöf space.
Proof
We have:
So if $S$ is countable, $T$ is a Lindelöf space.
$\blacksquare$
Also see
Sources
- 1978: Lynn Arthur Steen and J. Arthur Seebach, Jr.: Counterexamples in Topology (2nd ed.) ... (previous) ... (next): Part $\text {II}$: Counterexamples: $2$. Countable Discrete Topology: $8$