Talk:Fundamental group

The article claims that the fundamental group functor preserves all coproducts. This is, in general, false: a counterexample is given by the Hawaiian earring. Michael Lee Baker (talk) 05:36, 3 April 2014 (UTC)

Ouch, from the Hawaiian earring article:

G contains additional elements which arise from loops whose image is not contained in finitely many of the Hawaiian earring's circles; in fact, some of them are surjective. For example, the path that on the interval [2⁻ⁿ, 2⁻⁽ⁿ⁻¹⁾] circumnavigates the nth circle.

I guess for the coproduct to result you need base points to have contractible neighborhoods or something like that? This error goes way back to 2006. --Ørjan (talk) 09:18, 3 April 2014 (UTC)

Oh well, I've changed it to say locally contractible, I'm pretty sure that's enough. --Ørjan (talk) 09:23, 6 April 2014 (UTC)

Just turn on dark mode and go through the images. If it has LaTeX in the description, the maths symbols will render with a white background. Could someone do something about it and/or give me a quick guide on how I could fix it? Nihilux (talk) 01:49, 20 August 2025 (UTC)

The fundamental group is given here in higher dimension. I think that this article is exactly the one where the fundamental group of RP¹ has to be given.

I have read in many places on the Web that this fundamental group is Z because RP¹ and S¹ are homeomorphic topological spaces. I think that here is the right place to give (or to refer to) the indisputable solution.

( My intuition is that this fundamental group is Z x Z/2Z ... ) ~2025-29604-26 (talk) 13:06, 23 November 2025 (UTC)

After reflection I prefer the semi-direct product of Z and Z/2Z (which is isomorphic to the free product Z/2Z * Z/2Z), but certainly not Z alone. ~2025-29604-26 (talk) 15:24, 24 November 2025 (UTC)