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Published in:
2017 | OriginalPaper | Chapter
An Observation of the Subspaces of
Author : Yoshihiro Sawano
Published in: Generalized Functions and Fourier Analysis
Publisher: Springer International Publishing
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The spaces $$ \mathcal{S}^{\prime}/\mathcal{P} $$ equipped with the quotient topology and $$ \mathcal{S}^{\prime}_\infty $$ 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 [5], we give an alternative proof of this fact and then we extend this proposition so that we can include some related function spaces.