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Mar 25 at 9:19 comment added André Henriques @W.Rether Yes. The inclusion of smooth maps into continuous maps is a homotopy equivalence (that's a general fact about maps between smooth manifolds). The thing you're asking is a consequence: so yes, the inclusion of Gr into continuous maps a homotopy equivalence.
Mar 22 at 15:53 history bounty ended W.Rether
Mar 15 at 15:16 comment added W.Rether Thanks! Is the inclusion of Gr into continuous maps a homotopy equivalence?
Mar 15 at 14:21 history edited André Henriques CC BY-SA 4.0
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Mar 15 at 11:49 history answered André Henriques CC BY-SA 4.0