Samuele

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 Name Samuele Member for 1 year Seen May 16 at 17:09 Website Location Pisa, Italy Age 28
PhD student in Complex Analysis and Geometry, interested in singular complex spaces (and in finding a post-doc position, in the immediate :P).
 Apr7 comment Every continuous function is homotopic to a locally Lipschitz oneYes, 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? Apr7 revised Every continuous function is homotopic to a locally Lipschitz oneminor but meaningful mistakes corrected Apr7 awarded ● Nice Question Apr7 revised Every continuous function is homotopic to a locally Lipschitz oneAdded some further details (EDIT and ADDENDUM) Apr7 comment Every continuous function is homotopic to a locally Lipschitz oneWell, 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? Apr7 comment Every continuous function is homotopic to a locally Lipschitz oneFirst 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? Apr5 asked Every continuous function is homotopic to a locally Lipschitz one Dec17 comment Linear (in)dependence of minors of a matrixYou are welcome! Prego. Dec16 awarded ● Commentator Dec16 comment Space of sections of a fibre bundle with non-compact base spaceHmm 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... Dec16 answered Linear (in)dependence of minors of a matrix Dec16 asked Function of the incremental ratio tends weakly to a distribution