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Baire's Category Theorem and Some Spaces Generated from Real Normed Space1

. Real normed space. Formalized Mathematics , 2(1):111-115, 1991. [19] Bartłomiej Skorulski. First-countable, sequential, and Frechet spaces. Formalized Mathematics , 7(1):81-86, 1998. [20] Bartłomiej Skorulski. The sequential closure operator in sequential and Frechet spaces. Formalized Mathematics , 8(1):47-54, 1999. [21] Andrzej Trybulec. Subsets of complex numbers. To appear in Formalized Mathematics. [22] Andrzej Trybulec. Domains and their Cartesian

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Continuity of Bounded Linear Operators on Normed Linear Spaces

Ohkubo, and Yasunari Shidama. The continuous functions on normed linear spaces. Formalized Mathematics , 12( 3 ):269–275, 2004. [10] Hiroyuki Okazaki, Noboru Endou, and Yasunari Shidama. Cartesian products of family of real linear spaces. Formalized Mathematics , 19( 1 ):51–59, 2011. doi:10.2478/v10037-011-0009-2. [11] Yasunari Shidama. Banach space of bounded linear operators. Formalized Mathematics , 12( 1 ):39–48, 2004. [12] Yasunari Shidama. The series on Banach algebra. Formalized Mathematics , 12( 2 ):131–138, 2004. [13] Kosaku Yoshida

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Formalization of the Data Encryption Standard

Yasuho Mizuhara. Binary arithmetics. Formalized Mathematics , 4( 1 ):83-86, 1993. [15] U.S. Department of Commerce/National Institute of Standards and Technology. Fips pub 46-3, data encryption standard (DES). http://csrc.nist.gov/publications/fips/-fips46-3/fips46-3.pdf. Federal Information Processing Standars Publication , 1999. [16] Andrzej Trybulec. Domains and their Cartesian products. Formalized Mathematics , 1( 1 ):115-122, 1990. [17] Michał J. Trybulec. Integers. Formalized Mathematics , 1( 3 ):501-505, 1990

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Complete Spaces

. [22] Beata Padlewska. Families of sets. Formalized Mathematics , 1(1):147-152, 1990. [23] Beata Padlewska and Agata Darmochwał. Topological spaces and continuous functions. Formalized Mathematics , 1(1):223-230, 1990. [24] Andrzej Trybulec. Domains and their Cartesian products. Formalized Mathematics , 1(1):115-122, 1990. [25] Michał Trybulec. Formal languages - concatenation and closure. Formalized Mathematics , 15(1):11-15, 2007. [26] Zinaida Trybulec

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Towards the Construction of a Model of Mizar Concepts

Cartesian products. Formalized Mathematics , 1(1):115-122, 1990. [34] Andrzej Trybulec. Enumerated sets. Formalized Mathematics , 1(1):25-34, 1990. [35] Andrzej Trybulec. Tuples, projections and Cartesian products. Formalized Mathematics , 1(1):97-105, 1990. [36] Andrzej Trybulec. Many-sorted sets. Formalized Mathematics , 4(1):15-22, 1993. [37] Andrzej Trybulec. Many sorted algebras. Formalized Mathematics , 5(1):37-42, 1996. [38] Andrzej

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The Real Vector Spaces of Finite Sequences are Finite Dimensional

(2):329-334, 1990. [25] Andrzej Trybulec. Domains and their Cartesian products. Formalized Mathematics , 1(1):115-122, 1990. [26] Wojciech A. Trybulec. Basis of real linear space. Formalized Mathematics , 1(5):847-850, 1990. [27] Wojciech A. Trybulec. Binary operations on finite sequences. Formalized Mathematics , 1(5):979-981, 1990. [28] Wojciech A. Trybulec. Linear combinations in real linear space. Formalized Mathematics , 1(3):581-588, 1990

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Solutions of Linear Equations

field. Formalized Mathematics , 15(4):199-211, 2007. [18] Karol Pαk and Andrzej Trybulec. Laplace expansion. Formalized Mathematics , 15(3):143-150, 2007. [19] Andrzej Trybulec. Domains and their Cartesian products. Formalized Mathematics , 1(1):115-122, 1990. [20] Wojciech A. Trybulec. Basis of vector space. Formalized Mathematics , 1(5):883-885, 1990. [21] Wojciech A. Trybulec. Groups. Formalized Mathematics , 1(5):821-827, 1990. [22

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Brouwer Fixed Point Theorem for Simplexes

Trybulec. Domains and their Cartesian products. Formalized Mathematics , 1( 1 ):115-122, 1990. Andrzej Trybulec. A Borsuk theorem on homotopy types. Formalized Mathematics , 2( 4 ):535-545, 1991. Michał J. Trybulec. Integers. Formalized Mathematics , 1( 3 ):501-505, 1990. Wojciech A. Trybulec. Vectors in real linear space. Formalized Mathematics , 1( 2 ):291-296, 1990. Zinaida Trybulec. Properties of subsets. Formalized Mathematics , 1( 1 ):67-71, 1990

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Jordan Matrix Decomposition

. [26] Karol Pąk. Eigenvalues of a linear transformation. Formalized Mathematics , 16(4):289-295, 2008. [27] Karol Pąk. Linear map of matrices. Formalized Mathematics , 16(3):269-275, 2008. [28] Andrzej Trybulec. Binary operations applied to functions. Formalized Mathematics , 1(2):329-334, 1990. [29] Andrzej Trybulec. Domains and their Cartesian products. Formalized Mathematics , 1(1):115-122, 1990. [30] Wojciech A. Trybulec. Groups. Formalized Mathematics , 1

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Groups – Additive Notation

] Beata Padlewska and Agata Darmochwał. Topological spaces and continuous functions. Formalized Mathematics , 1(1):223-230, 1990. [31] Alexander Yu. Shibakov and Andrzej Trybulec. The Cantor set. Formalized Mathematics , 5(2):233-236, 1996. [32] Andrzej Trybulec. A Borsuk theorem on homotopy types. Formalized Mathematics , 2(4): 535-545, 1991. [33] Andrzej Trybulec. Domains and their Cartesian products. Formalized Mathematics , 1(1): 115-122, 1990. [34] Andrzej Trybulec. Enumerated sets. Formalized

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