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Semiring of Sets: Examples

, projections and Cartesian products. Formalized Mathematics, 1(1):97-105, 1990. [16] Andrzej Trybulec. On the sets inhabited by numbers. Formalized Mathematics, 11(4): 341-347, 2003. [17] Andrzej Trybulec and Agata Darmochwał. Boolean domains. Formalized Mathematics, 1 (1):187-190, 1990. [18] Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990. [19] Edmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1 (1):73-83, 1990.

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Free Magmas

):147-152, 1990. [14] Konrad Raczkowski and Paweł Sadowski. Equivalence relations and classes of abstraction. Formalized Mathematics , 1( 3 ):441-444, 1990. [15] Andrzej Trybulec. Tuples, projections and Cartesian products. Formalized Mathematics , 1( 1 ):97-105, 1990. [16] Andrzej Trybulec. Moore-Smith convergence. Formalized Mathematics , 6( 2 ):213-225, 1997. [17] Wojciech A. Trybulec and Michał J. Trybulec. Homomorphisms and isomorphisms of groups. Quotient

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Banach’s Continuous Inverse Theorem and Closed Graph Theorem

Mathematics , 1( 2 ):335-342, 1990. [10] Isao Miyadera. Functional Analysis . Riko-Gaku-Sya, 1972. [11] Takaya Nishiyama, Keiji Ohkubo, and Yasunari Shidama. The continuous functions on normed linear spaces. Formalized Mathematics , 12( 3 ):269-275, 2004. [12] 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. [13] Beata Padlewska and Agata Darmochwał. Topological spaces and

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Alexandroff One Point Compactification

(1):223-230, 1990. [14] Andrzej Trybulec. Domains and their Cartesian products. Formalized Mathematics , 1(1):115-122, 1990. [15] Andrzej Trybulec. Tarski Grothendieck set theory. Formalized Mathematics , 1(1):9-11, 1990. [16] Zinaida Trybulec. Properties of subsets. Formalized Mathematics , 1(1):67-71, 1990. [17] Edmund Woronowicz. Relations and their basic properties. Formalized Mathematics , 1(1):73-83, 1990. [18] Edmund Woronowicz. Relations

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Complex Integral

-801, 1990. [13] Konrad Raczkowski and Paweł Sadowski. Topological properties of subsets in real numbers. Formalized Mathematics , 1( 4 ):777-780, 1990. [14] Yasunari Shidama and Artur Korniłowicz. Convergence and the limit of complex sequences. Series. Formalized Mathematics , 6( 3 ):403-410, 1997. [15] Andrzej Trybulec. Tuples, projections and Cartesian products. Formalized Mathematics , 1( 1 ):97-105, 1990. [16] Zinaida Trybulec. Properties of subsets. Formalized

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Term Context

of morphisms. Formalized Mathematics , 6(2):303–310, 1997. [7] Grzegorz Bancerek. Tarski’s classes and ranks. Formalized Mathematics , 1(3):563–567, 1990. [8] Grzegorz Bancerek. Cartesian product of functions. Formalized Mathematics , 2(4):547– 552, 1991. [9] Grzegorz Bancerek. Institution of many sorted algebras. Part I: Signature reduct of an algebra. Formalized Mathematics , 6(2):279–287, 1997. [10] Grzegorz Bancerek. Free term algebras. Formalized Mathematics , 20(3):239–256, 2012. doi:10.2478/v10037-012-0029-6. [11] Grzegorz Bancerek. Terms over

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Introduction to Matroids

linear map. Formalized Mathematics , 5(3):339-345, 1996. [14] Adam Naumowicz. On Segre's product of partial line spaces. Formalized Mathematics , 9(2):383-390, 2001. [15] Beata Padlewska. Families of sets. Formalized Mathematics , 1(1):147-152, 1990. [16] Beata Padlewska and Agata Darmochwał. Topological spaces and continuous functions. Formalized Mathematics , 1(1):223-230, 1990. [17] Andrzej Trybulec. Domains and their Cartesian products. Formalized

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Isometric Differentiable Functions on Real Normed Space

spaces. Formalized Mathematics, 1(2):335-342, 1990. [14] Takaya Nishiyama, Keiji Ohkubo, and Yasunari Shidama. The continuous functions on normed linear spaces. Formalized Mathematics, 12(3):269-275, 2004. [15] 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. [16] Jan Popiołek. Real normed space. Formalized Mathematics, 2(1):111-115, 1991. [17] Laurent Schwartz. Cours d

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Bertrand’s Ballot Theorem

(4):755–760, 1990. [17] M. Renault. Four proofs of the ballot theorem. Mathematics Magazine , 80(5):345–352, December 2007. [18] Andrzej Trybulec. Domains and their Cartesian products. Formalized Mathematics , 1(1): 115–122, 1990. [19] Andrzej Trybulec. Enumerated sets. Formalized Mathematics , 1(1):25–34, 1990. [20] Andrzej Trybulec. On the decomposition of finite sequences. Formalized Mathematics , 5 (3):317–322, 1996. [21] Andrzej Trybulec. Binary operations applied to functions. Formalized Mathematics , 1 (2):329–334, 1990. [22] Wojciech A. Trybulec. Non

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The Sylow Theorems

and some of their properties - part I. Formalized Mathematics , 2(5):623-627, 1991. [18] Andrzej Trybulec. Subsets of complex numbers. To appear in Formalized Mathematics. [19] Andrzej Trybulec. Domains and their Cartesian products. Formalized Mathematics , 1(1):115-122, 1990. [20] Andrzej Trybulec. Tarski Grothendieck set theory. Formalized Mathematics , 1(1):9-11, 1990. [21] Michał J. Trybulec. Integers. Formalized Mathematics , 1(3):501-505, 1990

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