<abstract xml:lang="en" xmlns="http://www.w3.org/1999/xhtml"><p>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.</p></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.

Baire's Category Theorem and Some Spaces Generated from Real Normed Space<sup>1</sup>

Gifu National College of Technology, Gifu, Japan

Formalized Mathematics

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

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...

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

Published Online: Jun 13, 2008

Page range: 213 - 219

DOI: https://doi.org/10.2478/v10037-006-0024-x

This content is open access.

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

Published Online: Jun 13, 2008

Page range: 213 - 219

DOI: https://doi.org/10.2478/v10037-006-0024-x

This content is open access.

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