  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 $0\leq
r<s\leq\infty$ 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.
