Samuele
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Registered User
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PhD student in Complex Analysis and Geometry, interested in singular complex spaces (and in finding a post-doc position, in the immediate :P).
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Apr 7 |
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Every continuous function is homotopic to a locally Lipschitz one Yes, I wrote in a hurry: 1. the sequence should be the same for any couple of points 2. compact infinite dimensional spaces or manifolds modeled on nice linear spaces (the or was missing). Anyway, could you give a reference for the statement in your first comment? |
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Apr 7 |
revised |
Every continuous function is homotopic to a locally Lipschitz one minor but meaningful mistakes corrected |
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Apr 7 |
awarded | ● Nice Question |
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Apr 7 |
revised |
Every continuous function is homotopic to a locally Lipschitz one Added some further details (EDIT and ADDENDUM) |
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Apr 7 |
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Every continuous function is homotopic to a locally Lipschitz one Well, I assume my metric space to be complete and with a weak property of separability (for any two point $x,\ y$ there exists a sequence of $1$-Lip maps $(\phi_h)$ such that $d(x,y)=\sup_h |\phi_h(x)-\phi_h(y)|$). But obviously I don't expect that every of each spaces has a metric such that my request is satisfied. I think I could ask the following: is it true for manifolds? does it remain true if we allow singularities? which ones? is it true for infinite dimensional manifolds (maybe compact)? for Banachian or Hilbertian compact manifolds, at least? |
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Apr 7 |
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Every continuous function is homotopic to a locally Lipschitz one First of all, thank you. So, finite (geometric) simmplicial complexes work. Why do you need them to be finite? About the counterexample, that's interesting! But I was kind of expecting something like that: that's why I asked for a class of metric spaces, which come together with their distances. Another way to put the question could be to ask for a class of topological spaces which can be endowed with a distance (inducing their topology, hence metrizable spaces) so that the property holds. Could it be the case that CW-complexes do work? |
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Apr 5 |
asked | Every continuous function is homotopic to a locally Lipschitz one |
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Dec 17 |
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Linear (in)dependence of minors of a matrix You are welcome! Prego. |
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Dec 16 |
awarded | ● Commentator |
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Dec 16 |
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Space of sections of a fibre bundle with non-compact base space Hmm maybe the fact is (I didn't read the articles, so I'm just guessing) that for a non compact base manifold, the Fréchet structures you obtain are not tamely equivalent... |
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Dec 16 |
answered | Linear (in)dependence of minors of a matrix |
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Dec 16 |
asked | Function of the incremental ratio tends weakly to a distribution |
