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Formalized Mathematics

2011 | 19 | 1 | 51-59

Cartesian Products of Family of Real Linear Spaces

EN

Abstrakty

EN
In this article we introduced the isomorphism mapping between cartesian products of family of linear spaces [4]. Those products had been formalized by two different ways, i.e., the way using the functor [:X, Y:] and ones using the functor "product". By the same way, the isomorphism mapping was defined between Cartesian products of family of linear normed spaces also.

51-59

wydano
2011-01-01
online
2011-07-18

Twórcy

autor
• Shinshu University, Nagano, Japan
autor
• Nagano National College of Technology, Japan
autor
• Shinshu University, Nagano, 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] Nicolas Bourbaki. Topological vector spaces: Chapters 1-5. Springer, 1981.
• [5] Czesław Byliński. Binary operations. Formalized Mathematics, 1(1):175-180, 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] Noboru Endou, Yasunari Shidama, and Keiichi Miyajima. The product space of real normed spaces and its properties. Formalized Mathematics, 15(3):81-85, 2007, doi:10.2478/v10037-007-0010-y.[Crossref]
• [13] Beata Padlewska and Agata Darmochwał. Topological spaces and continuous functions. Formalized Mathematics, 1(1):223-230, 1990.
• [14] Jan Popiołek. Real normed space. Formalized Mathematics, 2(1):111-115, 1991.
• [15] Yasunari Shidama. Banach space of bounded linear operators. Formalized Mathematics, 12(1):39-48, 2004.
• [16] Andrzej Trybulec. Domains and their Cartesian products. Formalized Mathematics, 1(1):115-122, 1990.
• [17] Wojciech A. Trybulec. Pigeon hole principle. Formalized Mathematics, 1(3):575-579, 1990.
• [18] Wojciech A. Trybulec. Vectors in real linear space. Formalized Mathematics, 1(2):291-296, 1990.
• [19] Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990.
• [20] Edmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1(1):73-83, 1990.