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Mar 5, 2021 at 17:04 comment added Jeremy Brazas Absolutely! This argument extends to show that every locally path-connected, semilocally simply connected Lindelof space has a countable fundamental group!
Mar 5, 2021 at 12:34 vote accept Johnny El Curvas
Mar 5, 2021 at 12:34 comment added Johnny El Curvas I think this is definitely easier than proving "statement 4". I like the argument! It definitely reminds me of the proof of countability of $\pi_{1}(M)$, when $M$ is a manifold. Thank you very much!
Mar 4, 2021 at 15:11 history edited Jeremy Brazas CC BY-SA 4.0
fixed a couple of small notational errors/typos
Mar 3, 2021 at 18:46 history edited Jeremy Brazas CC BY-SA 4.0
corrected definition of gama_n
Mar 3, 2021 at 17:46 history edited Jeremy Brazas CC BY-SA 4.0
deleted 7 characters in body
Mar 3, 2021 at 17:26 history answered Jeremy Brazas CC BY-SA 4.0