My understanding is limited and I'm trying to learn more about how homotopy forms the notion of equivalence. I can grasp its definition as "continuous", but my understanding of homotopy falls away in spaces that are discrete. How does the mapping actually work?
2026-05-15 06:29:16.1778826556
Do homotopy equivalences operate over discrete spaces?
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Two discrete spaces are homotopy equivalent if and only if they have the same number of points. Any function whose domain is discrete is automatically continuous, and two functions $X \to Y$ for discrete $Y$ are homotopic if and only if they are equal.
(I'm not sure I understood your question, let me know if that clears things up or not.)