# Baire's Category Theorem and Some Spaces Generated from Real Normed Space 1

Noboru Endou; Yasunari Shidama; Katsumasa Okamura

Formalized Mathematics (2006)

- Volume: 14, Issue: 4, page 213-219
- ISSN: 1426-2630

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topNoboru Endou, Yasunari Shidama, and Katsumasa Okamura. " Baire's Category Theorem and Some Spaces Generated from Real Normed Space 1 ." Formalized Mathematics 14.4 (2006): 213-219. <http://eudml.org/doc/267064>.

@article{NoboruEndou2006,

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.},

author = {Noboru Endou, Yasunari Shidama, Katsumasa Okamura},

journal = {Formalized Mathematics},

language = {eng},

number = {4},

pages = {213-219},

title = { Baire's Category Theorem and Some Spaces Generated from Real Normed Space 1 },

url = {http://eudml.org/doc/267064},

volume = {14},

year = {2006},

}

TY - JOUR

AU - Noboru Endou

AU - Yasunari Shidama

AU - Katsumasa Okamura

TI - Baire's Category Theorem and Some Spaces Generated from Real Normed Space 1

JO - Formalized Mathematics

PY - 2006

VL - 14

IS - 4

SP - 213

EP - 219

AB - 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.

LA - eng

UR - http://eudml.org/doc/267064

ER -

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## Citations in EuDML Documents

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- Kazuhisa Nakasho, Noboru Endou, Separability of Real Normed Spaces and Its Basic Properties
- Keiko Narita, Yasunari Shidama, Noboru Endou, Weak Convergence and Weak Convergence

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