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Aug
14
comment Homology of Euclidean space $H_n(\mathbb{R}^m)$
@gary: thanks anyway, for trying!
Aug
14
revised Homology of Euclidean space $H_n(\mathbb{R}^m)$
added 79 characters in body
Aug
13
answered Homology of Euclidean space $H_n(\mathbb{R}^m)$
Aug
13
revised Homology of Euclidean space $H_n(\mathbb{R}^m)$
added 115 characters in body
Aug
13
accepted Question about deformation retracts and neighbourhoods
Aug
13
asked Homology of Euclidean space $H_n(\mathbb{R}^m)$
Aug
11
awarded  Tumbleweed
Aug
11
accepted False proof of $H_0 ( X) = 0$
Aug
10
comment False proof of $H_0 ( X) = 0$
Ok, Chris maybe you can make your comment into an answer so that I can accept it. Many thanks for your help!
Aug
10
comment False proof of $H_0 ( X) = 0$
Oh!! $\{ c\}$, $\{c + c\}$, $\dots$ are all different elements of $H_0 (X)$. That's what you're saying?
Aug
10
comment False proof of $H_0 ( X) = 0$
Because it's a group and it only has one element, so that element has got to be neutral element otherwise it's not a group.
Aug
10
asked False proof of $H_0 ( X) = 0$
Aug
10
comment Question about the sum of chain groups
Yes I do : ) (some more characters)
Aug
10
comment Question about the sum of chain groups
No! I think I finally got it: for the boundary map $\partial: C(X) = C (A \cup B) \rightarrow C(X)$ it holds that $\partial ( C ( A + B) ) \subset C( A + B)$. And the reason why is because $C(A)$ and $C(B)$ are chain complexes.
Aug
10
comment Question about the sum of chain groups
Actually no, I think you meant to write "...Since the boundary map of $C(A + B)$ restricts to $C(A + B)$ (why?),..."!
Aug
10
comment Question about the sum of chain groups
I think you meant to write "...Since the boundary map of $C(A \cup B)$ restricts to $C(A \cup B)$ (why?),...", because e.g. $\sigma$ in the picture is a simplex in $C(A\cup B)$ with 2 of its 3 boundaries in $C(A \cup B) - C(A + B)$.
Aug
10
comment Question about the sum of chain groups
GeoGebra looks really good, I had never heard of it before. I do all my drawing on paper, how old fashioned : D
Aug
9
comment Computing $H_1(X)$ using Hurewicz
Hey, thanks! I think I'm using Hurewicz theorem, maybe it's called Poincare for $n=1$ : )
Aug
9
comment Question about the sum of chain groups
I wish I could give you more up votes for all this effort you put into writing this answer.
Aug
9
comment Question about the sum of chain groups
Actually, I do draw pictures. I've been following your advice on more than one occasion... and I appreciate your help! I think I should chuck Hatcher, every now and again there is a passage in it that is utterly unhelpful : (