Baire's Category Theorem and Some Spaces Generated from Real Normed Space1

Noboru Endou; Yasunari Shidama; Katsumasa Okamura

doi:10.2478/v10037-006-0024-x

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Baire's Category Theorem and Some Spaces Generated from Real Normed Space1

Formalized Mathematics

Volume 14 (2006): Issue 4 (December 2006)

By: Noboru Endou, Yasunari Shidama and Katsumasa Okamura

Open Access

|Jun 2008

Abstract

As application of complete metric space, we proved a Baire's category theorem. Then we defined some spaces generated from real normed space and discussed each of them. In the second section, we showed the equivalence of convergence and the continuity of a function. In other sections, we showed some topological properties of two spaces, which are topological space and linear topological space generated from real normed space.

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Articles in this issue

DOI: https://doi.org/10.2478/v10037-006-0024-x | Journal eISSN: 1898-9934 | Journal ISSN: 1426-2630

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Language: English

Page range: 213 - 219

Published on: Jun 13, 2008

Published by: University of Białystok

In partnership with: Paradigm Publishing Services

Publication frequency: 1 issue per year

Related subjects:

Mathematics,

Logic and set theory,

Computer sciences,

Artificial intelligence

© 2008 Noboru Endou, Yasunari Shidama, Katsumasa Okamura, published by University of Białystok
This work is licensed under the Creative Commons License.

Volume 14 (2006): Issue 4 (December 2006)