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Dec 5 at 15:12 comment added Jeremy Brazas The fundamental group of a one-dimensional metric space $X$ is free if and only if $X$ is semilocally simply connected. This one is not, so it's not free. This is why I had commented on it being residually and locally free.
Dec 5 at 5:56 comment added Carl-Fredrik Nyberg Brodda It would be nice to know whether $\pi_1(X)$ is free or not.
Dec 4 at 19:54 history edited Jeremy Brazas CC BY-SA 4.0
revised projection notation.
Dec 4 at 19:04 history edited Jeremy Brazas CC BY-SA 4.0
added 2 characters in body
Dec 4 at 19:02 vote accept Dominic van der Zypen
Dec 4 at 18:45 history answered Jeremy Brazas CC BY-SA 4.0