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- W3080963300 abstract "Let $M, N$ the be smooth manifolds, $mathcal{C}^{r}(M,N)$ the space of ${C}^{r}$ maps endowed with weak $C^{r}$ Whitney topology, and $mathcal{B} subset mathcal{C}^{r}(M,N)$ an open subset. It is proved that for $0leq r<sleqinfty$ the inclusion $mathcal{B} cap mathcal{C}^{s}(M,N) subset mathcal{B}$ is a weak homotopy equivalence. It is also established a parametrized variant of such a result. In particular, it is shown that for a compact manifold $M$, the inclusion of the space of $mathcal{C}^{s}$ isotopies $[0,1]times M to M$ fixed near ${0,1}times M$ into the space of loops $Omega(mathcal{D}^{r}(M), mathrm{id}_{M})$ of the group of $mathcal{C}^{r}$ diffeomorphisms of $M$ at $mathrm{id}_{M}$ is a weak homotopy equivalence." @default.
- W3080963300 created "2020-09-01" @default.
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- W3080963300 date "2020-09-13" @default.
- W3080963300 modified "2023-10-09" @default.
- W3080963300 title "Smooth approximations and their applications to homotopy types" @default.
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- W3080963300 doi "https://doi.org/10.15673/tmgc.v13i2.1781" @default.
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