A simple example of Lindelöf space.


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 non-compact example.


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Updated on December 22, 2020


  • Walner
    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
      Forever Mozart over 10 years
      The reals are Lindelof. In fact any second countable space is Lindelof.
    • MyUserIsThis
      MyUserIsThis over 10 years
      I guess you want an example in which the subcovers are countable but not finite, do you? You should put that in the question.