Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

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.

share|improve this question
2  
The reals are Lindelof. In fact any second countable space is Lindelof. –  Tom Cruise Jun 27 '13 at 22:13
1  
I guess you want an example in which the subcovers are countable but not finite, do you? You should put that in the question. –  MyUserIsThis Jun 27 '13 at 22:14

1 Answer 1

up vote 2 down vote accepted

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.

share|improve this answer

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.