# Notes on topological vector spaces

@article{Semmes2003NotesOT, title={Notes on topological vector spaces}, author={S. Semmes}, journal={arXiv: Classical Analysis and ODEs}, year={2003} }

These are some informal notes concerning topological vector spaces, with a brief overview of background material and basic notions, and emphasis on examples related to classical analysis.

## 1,547 Citations

Notes on algebras and vector spaces of functions

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In this paper, we introduce and study the concept of ideal topological vector spaces.

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We introduce the notion of positivity for a real basic (1, 1) class in basic Bott-Chern cohomology group on foliated manifolds, and study the relationship between this positivity and the negativity…

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A topological vector space X over \(\mathbb{R}\) or \(\mathbb{C}\) is a vector space, which is also a topological space, in which the vector space operations are continuous.

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In this paper we present a new characterization of locally bounded topological vector spaces, which generalize earlier characterizations of Aoki [1] and Rolewicz [13]. Further we shall prove that…

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In this paper, we first introduce some function spaces, with certain locally convex topologies, closely related to the space of realvalued continuous functions on X, where X is a C-distinguished…

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