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The question is a special case of a previous question.

Let $M$ be a compact smooth manifold, then it is clear that $C^{\infty}(M)$ is a Frechet algebra with pointwise multiplication and a collection of semi-norm defined by $p_{\alpha}(f):=\sup_{\beta\leq\alpha}||\partial^{\beta}(f)||$.

Now let $E\to M$ be a $C^{\infty}$-fiber bundle with compact base and compact fiber. Then it is clear that $C^{\infty}(E)$, the space of smooth sections of the total space of the fiber bundle, is a Frechet $C^{\infty}(M)$-module.

My question is: is $C^{\infty}(E)$ always a projective Frechet $C^{\infty}(M)$-module?

I think this question is trivial for experts. Please let me know if there is any references or it the question is not suitable for mathoverflow.

The question is a special case of a previous question.

Let $M$ be a compact smooth manifold, then it is clear that $C^{\infty}(M)$ is a Frechet algebra with pointwise multiplication and a collection of semi-norm defined by $p_{\alpha}(f):=\sup_{\beta\leq\alpha}||\partial^{\beta}(f)||$.

Now let $E\to M$ be a $C^{\infty}$-fiber bundle with compact base and compact fiber. Then it is clear that $C^{\infty}(E)$, the space of smooth functions on the total space of the fiber bundle, is a Frechet $C^{\infty}(M)$-module.

My question is: is $C^{\infty}(E)$ always a projective Frechet $C^{\infty}(M)$-module?

I think this question is trivial for experts. Please let me know if there is any references or it the question is not suitable for mathoverflow.

The question is a special case of a previous question.

Let $M$ be a compact smooth manifold, then it is clear that $C^{\infty}(M)$ is a Frechet algebra with pointwise multiplication and a collection of semi-norm defined by $p_{\alpha}(f):=\sup_{\beta\leq\alpha}||\partial^{\beta}(f)||$.

Now let $E\to M$ be a $C^{\infty}$-fiber bundle with compact base and compact fiber. Then it is clear that $\Gamma^{\infty}(E)$, the space of smooth sections of the fiber bundle, is a Frechet $C^{\infty}(M)$-module.

My question is: is $C^{\infty}(E)$ always a projective Frechet $C^{\infty}(M)$-module?

I think this question is trivial for experts. Please let me know if there is any references or it the question is not suitable for mathoverflow.

The question is a special case of a previous question.

Let $M$ be a compact smooth manifold, then it is clear that $C^{\infty}(M)$ is a Frechet algebra with pointwise multiplication and a collection of semi-norm defined by $p_{\alpha}(f):=\sup_{\beta\leq\alpha}||\partial^{\beta}(f)||$.

Now let $E\to M$ be a $C^{\infty}$-fiber bundle with compact base and compact fiber. Then it is clear that $C^{\infty}(E)$, the space of smooth sections of the total space of the fiber bundle, is a Frechet $C^{\infty}(M)$-module.

My question is: is $C^{\infty}(E)$ always a projective Frechet $C^{\infty}(M)$-module?

I think this question is trivial for experts. Please let me know if there is any references or it the question is not suitable for mathoverflow.

The question is a special case of a previous question.

Let $M$ be a compact smooth manifold, then it is clear that $C^{\infty}(M)$ is a Frechet algebra with pointwise multiplication and a collection of semi-norm defined by $p_{\alpha}(f):=\sup_{\beta\leq\alpha}||\partial^{\beta}(f)||$.

Now let $E\to M$ be a $C^{\infty}$-fiber bundle with compact base and compact fiber. Then it is clear that $C^{\infty}(E)$ is a Frechet $C^{\infty}(M)$-module.

My question is: is $C^{\infty}(E)$ always a projective Frechet $C^{\infty}(M)$-module?

I think this question is trivial for experts. Please let me know if there is any references or it the question is not suitable for mathoverflow.

The question is a special case of a previous question.

Let $M$ be a compact smooth manifold, then it is clear that $C^{\infty}(M)$ is a Frechet algebra with pointwise multiplication and a collection of semi-norm defined by $p_{\alpha}(f):=\sup_{\beta\leq\alpha}||\partial^{\beta}(f)||$.

Now let $E\to M$ be a $C^{\infty}$-fiber bundle with compact base and compact fiber. Then it is clear that $\Gamma^{\infty}(E)$, the space of smooth sections of the fiber bundle, is a Frechet $C^{\infty}(M)$-module.

My question is: is $C^{\infty}(E)$ always a projective Frechet $C^{\infty}(M)$-module?

I think this question is trivial for experts. Please let me know if there is any references or it the question is not suitable for mathoverflow.