# Algebraic Topology

Can we help me next tags:

1. Let $Y$ vector topological space and $A \subseteq Y$ convex set. Prove that any two continuous mappings $f,g : X \to A$ homotopic, where $X$ is an arbitrary topological space.
2. Prove that every interval $(a, b)$ homotopy equivalent point.
3. Let $X$ be a contractible space. Prove that the space $X$ every two times with the same beginning and end homotopic (rel $\{0,1\}$).
4. Prove that two topological spaces one of which is attached, and the other can not be unlinked homotopy equivalent.
5. Show that the fundamental group of the space $\mathbb R^n$ , $n\geq 1$, trivial.
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Hope this helps.

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