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Formalized Mathematics

(a computer assisted approach)

Editor-in-Chief: Matuszewski, Roman

4 Issues per year


SCImago Journal Rank (SJR) 2015: 0.134
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ISSN
1898-9934
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Volume 14, Issue 4 (Jan 2006)

Issues

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

Noboru Endou
  • Gifu National College of Technology, Gifu, Japan
/ Yasunari Shidama
  • Shinshu University, Nagano, Japan
/ Katsumasa Okamura
  • Shinshu University, Nagano, Japan
Published Online: 2008-06-13 | DOI: https://doi.org/10.2478/v10037-006-0024-x

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

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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About the article


Published Online: 2008-06-13

Published in Print: 2006-01-01


Citation Information: Formalized Mathematics, ISSN (Online) 1898-9934, ISSN (Print) 1426-2630, DOI: https://doi.org/10.2478/v10037-006-0024-x. Export Citation

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