# Tagged Questions

Two functions are homotopic, if one of them can by continuously deformed to another. This gives rise to an equivalence relation. A group called homotopy group can be obtained from the equivalence classes. The simplest homotopy group is fundamental group. Homotopy groups are important invariants in ...

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### any continuous function is null homotopic for convex set.

Let $X$ be a topological space. and suppose $B$ is a convex subset in $\mathbb{R}^n$. Prove that any continuous map $f: X \rightarrow B$ is null-homotopic. My strategy is following the defintion of ...
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### Example of building a classifying space

I'm reading some things about algebraic topology, and they mention the classifying space of a group $G$ as $BG$, but they doesn't build one, so I want to ask if someone knows where can I find the way ...
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### How to show the constant path is the identity element in fundamental group?

Let $X$ be a topological space and $q$ is a point in $X$. Denote the fundamental group of $X$ based at $q$ by $\pi _1(X,q)$. Then how should I verify that the constant path $c_q(s)\equiv q$ is the ...
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### Expositions of Postkinov Towers

I am giving a lecture on Postkinov towers and I want to teach the students a lesson :). These students have seen local coefficients, spectral sequences and cohomology operations at the level of ...
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### $1_{S^{n-1}} \simeq$ to a constant map

I have to show that $\exists\ \ f : D^n \rightarrow S^{n-1}$ with $f\circ i =1_{S^{n-1}} \iff 1_{S^{n-1}}$ is homotopic to a constant map. I don't know how to prove this. So, please help me in ...