The Product Space of Real Normed Spaces and its Properties

• Autorzy: Noboru Endou , Yasunari Shidama , Keiichi Miyajima
• Języki publikacji: EN

Abstrakty

EN

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

• Wydawca: De Gruyter Open
• Czasopismo: Formalized Mathematics
• Rocznik: 2007
• Tom: 15
• Numer: 3
• Strony: 81-85

Daty

wydano

2007-01-01

online

2008-06-09

Twórcy

autor

Noboru Endou

• Gifu National College of Technology, Japan

autor

Yasunari Shidama

• Shinshu University, Nagano, Japan

autor

Keiichi Miyajima

• Ibaraki University, Hitachi, Japan

Bibliografia

• [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.

Identyfikatory

DOI

10.2478/v10037-007-0010-y