What is the Homotopy geometrically?And what is path-homotopy?
If two real valued functions are homotopic to each other, then what can we say about the geometry behind this? It need not be equal function but what sort of functions they are?
2026-05-05 22:54:33.1778021673
what does Homotopy Tell?
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Homotopy doesn't really tell you much about the space, except $n$-connectedness and things like that. Path homotopy is nothing but homotopy of paths. As for the second question, the fundamental group of $\mathbf{R}^n$ vanishes. Therefore it is simply connected and hence any two real-valued maps are homotopic. I suggest reading Hatcher, Chapter 1.