We dont have CW complex merged yet, but I wanna write this down so i dont forget it:
Suppose we have a 1-dimensional manifold with boundary, WLOG connected. It's interior (I have never properly done anything with manifold, so idk if this is the proper name) must be S^1 or $\mathbb{R}$ https://math.stackexchange.com/questions/113705/the-only-1-manifolds-are-mathbb-r-and-s1
So all 1-manifold must be disjoint unions of $S^1, [0,1], (0,1), [0,1)$ all of which are are CW complexes.
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If we dont end up adding "half one euclidean", one can directly apply the general theorem that any top. manifold with dim =/= 4 is a CW complex.
Also we better refine #1753 in the following way: Embedabble in R + Locally connected => Topological n-manifold with boundary => Locally contractible
We dont have CW complex merged yet, but I wanna write this down so i dont forget it:
Suppose we have a 1-dimensional manifold with boundary, WLOG connected. It's interior (I have never properly done anything with manifold, so idk if this is the proper name) must be S^1 or$\mathbb{R}$ https://math.stackexchange.com/questions/113705/the-only-1-manifolds-are-mathbb-r-and-s1
So all 1-manifold must be disjoint unions of$S^1, [0,1], (0,1), [0,1)$ all of which are are CW complexes.
--
If we dont end up adding "half one euclidean", one can directly apply the general theorem that any top. manifold with dim =/= 4 is a CW complex.
Also we better refine #1753 in the following way: Embedabble in R + Locally connected => Topological n-manifold with boundary => Locally contractible