A simple example of Lindelöf space.
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The natural numbers with the discrete topology.
Given an open cover, $U_i$ let $U_n$ be some open set such that $n\in U_n$, then $\{U_n\mid n\in\Bbb N\}$ is a countable subcover.
Although simpler example, perhaps, would be any compact set. I still think that you may benefit from a noncompact example.
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Walner
Updated on December 22, 2020Comments

Walner almost 3 years
Somebody can to give me a simple example of Lindelöf space?
Note. Lindelöf space is a topological space in which every open cover has a countable subcover.

Forever Mozart over 10 yearsThe reals are Lindelof. In fact any second countable space is Lindelof.

MyUserIsThis over 10 yearsI guess you want an example in which the subcovers are countable but not finite, do you? You should put that in the question.
