# The Product Space of Real Normed Spaces and its Properties

Noboru Endou; Yasunari Shidama; Keiichi Miyajima

Formalized Mathematics (2007)

- Volume: 15, Issue: 3, page 81-85
- ISSN: 1426-2630

## Access Full Article

top## Abstract

top## How to cite

topNoboru Endou, Yasunari Shidama, and Keiichi Miyajima. "The Product Space of Real Normed Spaces and its Properties." Formalized Mathematics 15.3 (2007): 81-85. <http://eudml.org/doc/266533>.

@article{NoboruEndou2007,

abstract = {In this article, we define the product space of real linear spaces and real normed spaces. We also describe properties of these spaces.},

author = {Noboru Endou, Yasunari Shidama, Keiichi Miyajima},

journal = {Formalized Mathematics},

language = {eng},

number = {3},

pages = {81-85},

title = {The Product Space of Real Normed Spaces and its Properties},

url = {http://eudml.org/doc/266533},

volume = {15},

year = {2007},

}

TY - JOUR

AU - Noboru Endou

AU - Yasunari Shidama

AU - Keiichi Miyajima

TI - The Product Space of Real Normed Spaces and its Properties

JO - Formalized Mathematics

PY - 2007

VL - 15

IS - 3

SP - 81

EP - 85

AB - In this article, we define the product space of real linear spaces and real normed spaces. We also describe properties of these spaces.

LA - eng

UR - http://eudml.org/doc/266533

ER -

## References

top- [1] Grzegorz Bancerek. König's theorem. Formalized Mathematics, 1(3):589-593, 1990.
- [2] Grzegorz Bancerek. The ordinal numbers. Formalized Mathematics, 1(1):91-96, 1990.
- [3] Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Formalized Mathematics, 1(1):107-114, 1990.
- [4] Czesław Byliński. Binary operations. Formalized Mathematics, 1(1):175-180, 1990.
- [5] Czesław Byliński. The complex numbers. Formalized Mathematics, 1(3):507-513, 1990.
- [6] Czesław Byliński. Finite sequences and tuples of elements of a non-empty sets. Formalized Mathematics, 1(3):529-536, 1990.
- [7] Czesław Byliński. Functions and their basic properties. Formalized Mathematics, 1(1):55-65, 1990.
- [8] Czesław Byliński. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990.
- [9] Czesław Byliński. Some basic properties of sets. Formalized Mathematics, 1(1):47-53, 1990.
- [10] Czesław Byliński. The sum and product of finite sequences of real numbers. Formalized Mathematics, 1(4):661-668, 1990.
- [11] Agata Darmochwał. The Euclidean space. Formalized Mathematics, 2(4):599-603, 1991.
- [12] Jarosław Kotowicz. Convergent sequences and the limit of sequences. Formalized Mathematics, 1(2):273-275, 1990.
- [13] Jarosław Kotowicz. Real sequences and basic operations on them. Formalized Mathematics, 1(2):269-272, 1990.
- [14] Eugeniusz Kusak, Wojciech Leończuk, and Michał Muzalewski. Abelian groups, fields and vector spaces. Formalized Mathematics, 1(2):335-342, 1990.
- [15] Anna Lango and Grzegorz Bancerek. Product of families of groups and vector spaces. Formalized Mathematics, 3(2):235-240, 1992.
- [16] Beata Padlewska and Agata Darmochwał. Topological spaces and continuous functions. Formalized Mathematics, 1(1):223-230, 1990.
- [17] Jan Popiołek. Real normed space. Formalized Mathematics, 2(1):111-115, 1991.
- [18] Yasunari Shidama. Banach space of bounded linear operators. Formalized Mathematics, 12(1):39-48, 2004.
- [19] Andrzej Trybulec. Subsets of complex numbers. To appear in Formalized Mathematics.
- [20] Andrzej Trybulec. Tarski Grothendieck set theory. Formalized Mathematics, 1(1):9-11, 1990.
- [21] Wojciech A. Trybulec. Vectors in real linear space. Formalized Mathematics, 1(2):291-296, 1990.
- [22] Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990.
- [23] Edmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1(1):73-83, 1990.

## Citations in EuDML Documents

top## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.