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Apr
25
revised $\lim_{n\to \infty }\frac{a_{n+1}}{a_{n}}< 1$, $a_{_{n}}> 0$- does $a_{_{n}}$ converge?
Clarification added.
Apr
25
comment $\lim_{n\to \infty }\frac{a_{n+1}}{a_{n}}< 1$, $a_{_{n}}> 0$- does $a_{_{n}}$ converge?
@Didier: sorry, can you explain a bit more detailed, I can't find my mistake, even reading your comment above, thank you!
Apr
25
comment $\lim_{n\to \infty }\frac{a_{n+1}}{a_{n}}< 1$, $a_{_{n}}> 0$- does $a_{_{n}}$ converge?
@Didier, @Martin: I'm not proving that the limit is $0$!
Apr
25
revised $\lim_{n\to \infty }\frac{a_{n+1}}{a_{n}}< 1$, $a_{_{n}}> 0$- does $a_{_{n}}$ converge?
Clarification added.
Apr
25
answered $\lim_{n\to \infty }\frac{a_{n+1}}{a_{n}}< 1$, $a_{_{n}}> 0$- does $a_{_{n}}$ converge?
Apr
25
comment Fundamental Group of a finite set with discrete topology
@Theo: I assume you are using $S^1$ instead of $[0,1]$ because the question is about closed paths. Why do you have to choose a base point in the domain of the paths? Shouldn't you say "...since $S^1$ is connected, it must be mapped to this base point entirely....", where that base point is the one in $S$?
Apr
25
comment Fundamental Group of a finite set with discrete topology
@Theo: what's $S^1$? The unit circle?
Apr
23
comment Homotopy equivalence iff both spaces are deformation retracts
@Theo: thanks, that was a typo. I corrected it.
Apr
23
revised Homotopy equivalence iff both spaces are deformation retracts
added 13 characters in body
Apr
23
comment Simple set exercise seems not so simple
Nice answer!
Apr
23
answered Simple set exercise seems not so simple
Apr
22
comment Why is a finite CW complex compact?
@Dylan: Thanks. I think now I understand. A cell is the interior of a closed disk. @Dylan: Did you mean to write "...is to glue a disk along its boundary..."? Because if a cell is open then it doesn't have a boundary.
Apr
22
accepted Why is a finite CW complex compact?
Apr
21
comment Why is a finite CW complex compact?
But on page 5 he writes "open $n$-disk" where he explains how to construct a CW complex in step (2). He is attaching open disks!
Apr
21
asked Why is a finite CW complex compact?
Apr
21
comment Homotopy equivalence iff both spaces are deformation retracts
@Chris: thanks, but that uses "the preceding corollary". I'm going to read that but for now I needed something that doesn't use things that I don't know yet.
Apr
21
comment Homotopy equivalence iff both spaces are deformation retracts
@Theo: done! Although, it doesn't seem any more intuitive to me.
Apr
21
revised Homotopy equivalence iff both spaces are deformation retracts
Added detail in response to comment.; added 290 characters in body; edited body
Apr
19
revised Homotopy equivalence iff both spaces are deformation retracts
added 13 characters in body; deleted 5 characters in body
Apr
19
answered Homotopy equivalence iff both spaces are deformation retracts