# Tagged Questions

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### Question on homotopy

What is the relation between the definition of homotopy of two functions " a homotopy between two continuous functions $f$ and $g$ from a topological space $X$ to a topological space $Y$ is defined ...
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### Deformation retract of $\mathbb{R}^3$ minus a tetrahedron

Question from a past exam in an introductory course in algebraic topology. Call $X$ the space $\mathbb{R}^3$ minus the edges (one dimensional) of a tetrahedron. Does $X$ deformation retract onto a ...
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### Space of curves and differentiability

Let $A\subset\mathbb{R^2}$ be an open connected set, and $\Omega=\{c:[0,1]\rightarrow A| c\in C^1\textrm{ and } c(0)=c(1)\}$. Consider the $1$-form $\omega = F_1dx_1+F_2dx_2$ in $A$ such that ...
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### Lemma of Whitehead

this is the lemma of Whitehead And i really don't understand the proof How to see that $k$ is well defined (i.e how to write an element from $X\cup_{\varphi_i}e^{\lambda} , i=0,1$ ) and how to ...
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### The action of the group of deck transformation on the higher homotopy groups

This is for homework. I'm supposed to do exercise 4.1.4 in Hatchers "Algebraic Topology", which is to show that given a universal covering $p: \tilde{X} \to X$ of a path-connected space $X$, the ...