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

Abstract

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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.

How to cite

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Noboru 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 -

References

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Citations in EuDML Documents

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  1. Hideki Sakurai, Hisayoshi Kunimune, Yasunari Shidama, Uniform Boundedness Principle
  2. Kazuhisa Nakasho, Yuichi Futa, Yasunari Shidama, Topological Properties of Real Normed Space
  3. Hideki Sakurai, Hisayoshi Kunimune, Yasunari Shidama, Open Mapping Theorem
  4. Roland Coghetto, Summable Family in a Commutative Group
  5. Keiko Narita, Noboru Endou, Yasunari Shidama, Bidual Spaces and Reflexivity of Real Normed Spaces
  6. Kazuhisa Nakasho, Noboru Endou, Separability of Real Normed Spaces and Its Basic Properties
  7. Keiko Narita, Yasunari Shidama, Noboru Endou, Weak Convergence and Weak Convergence

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