# Tagged Questions

This tag is in the process of being removed; please do not add this tag to new questions. Rather, use tags that describe the subject of your question, like [calculus], [algebra-precalculus], etc. For more information, see meta: http://meta.math.stackexchange.com/questions/16425.

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### Prove that if $f:D^2\to D^2$ is a homeomorphism, then $f(S^1)=S^1$

I've already proved that set of points $z\in D^2$ such that $D^2-z$ is simply connected is precisely $S^1$. Now from this, I'm supposed to conclude that if $f:D^2\to D^2$ is a homeomorphism, then ...
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### Application of Dirichlet Theorem in AP to elementary number theory problems.

I have learnt this theorem in my class, however, "elementary" examples are very limited. (focusing more on analytic machinery) Are there any interesting applications to elementary number theory that ...
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### Products of homology groups

In the topology course I attend we work with the following, rather unusual definition of homology groups: For topological spaces $X,Y$ define the presheaf $\mathcal{F}_Y$ on $X$ as follows: Let ...
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### How many elements are there in total?

Suppose that we have a collection of 12 sets, each of which has 8 elements. Every pair of sets shares 6 elements, any collection of 3 sets shares 4 elements, and no collection of 4 sets shares any ...
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### Does convergence of $(a_{5n})$ and $(a_{n+1} - a_n)\rightarrow0$ imply convergence of $a_n$

As I wrote in the title: Does convergence of $(a_{5n})$ and the fact that $(a_{n+1} - a_n)\rightarrow0$ imply convergence of $a_n$. I understand that convergence of $(a_{5n})$ means that $(a_n)$can ...