An observation of the subspaces of ${\mathcal S}'$

Yoshihiro Sawano

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arXiv · 1603.07890

An observation of the subspaces of ${\mathcal S}'$

Yoshihiro Sawano

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Abstract

The spaces ${\mathcal S}'/{\mathcal P}$ equipped with the quotient topology and ${\mathcal S}'_\infty$ equipped with the weak-* topology are known to be homeomorphic, where ${\mathcal P}$ denotes the set of all polynomials. The proof is a combination of the fact in the textbook by Treves and the well-known bipolar theorem. In this paper by extending slightly the idea employed in \cite{NNS15}, we give an alternative proof of this fact and then we extend this proposition so that we can include some related function spaces.

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Yoshihiro Sawano. 2016-04-13. An observation of the subspaces of ${\mathcal S}'$. https://arxiv.org/abs/1603.07890

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