104 research outputs found
Convergent Filter Bases
AbstractWe are inspired by the work of Henri Cartan [16], Bourbaki [10] (TG. I Filtres) and Claude Wagschal [34]. We define the base of filter, image filter, convergent filter bases, limit filter and the filter base of tails (fr: filtre des sections).Rue de la Brasserie 5, 7100 La Louvière, BelgiumGrzegorz Bancerek. Cardinal numbers. Formalized Mathematics, 1(2):377-382, 1990.Grzegorz Bancerek. König’s theorem. Formalized Mathematics, 1(3):589-593, 1990.Grzegorz Bancerek. Complete lattices. Formalized Mathematics, 2(5):719-725, 1991.Grzegorz Bancerek. The fundamental properties of natural numbers. Formalized Mathematics, 1(1):41-46, 1990.Grzegorz Bancerek. The ordinal numbers. Formalized Mathematics, 1(1):91-96, 1990.Grzegorz Bancerek. Directed sets, nets, ideals, filters, and maps. Formalized Mathematics, 6(1):93-107, 1997.Grzegorz Bancerek. Prime ideals and filters. Formalized Mathematics, 6(2):241-247, 1997.Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Formalized Mathematics, 1(1):107-114, 1990.Grzegorz Bancerek, Noboru Endou, and Yuji Sakai. On the characterizations of compactness. Formalized Mathematics, 9(4):733-738, 2001.Nicolas Bourbaki. General Topology: Chapters 1-4. Springer Science and Business Media, 2013.Czesław Bylinski. Functions and their basic properties. Formalized Mathematics, 1(1): 55-65, 1990.Czesław Bylinski. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990.Czesław Bylinski. Basic functions and operations on functions. Formalized Mathematics, 1(1):245-254, 1990.Czesław Bylinski. Partial functions. Formalized Mathematics, 1(2):357-367, 1990.Czesław Bylinski. Some basic properties of sets. Formalized Mathematics, 1(1):47-53, 1990.Henri Cartan. Théorie des filtres. C. R. Acad. Sci., CCV:595-598, 1937.Marek Chmur. The lattice of natural numbers and the sublattice of it. The set of prime numbers. Formalized Mathematics, 2(4):453-459, 1991.Agata Darmochwał. Finite sets. Formalized Mathematics, 1(1):165-167, 1990.Adam Grabowski and Robert Milewski. Boolean posets, posets under inclusion and products of relational structures. Formalized Mathematics, 6(1):117-121, 1997.Gilbert Lee and Piotr Rudnicki. Dickson’s lemma. Formalized Mathematics, 10(1):29-37, 2002.Yatsuka Nakamura and Hisashi Ito. Basic properties and concept of selected subsequence of zero based finite sequences. Formalized Mathematics, 16(3):283-288, 2008. doi:10.2478/v10037-008-0034-y. [Crossref]Beata Padlewska. Families of sets. Formalized Mathematics, 1(1):147-152, 1990.Beata Padlewska and Agata Darmochwał. Topological spaces and continuous functions. Formalized Mathematics, 1(1):223-230, 1990.Alexander Yu. Shibakov and Andrzej Trybulec. The Cantor set. Formalized Mathematics, 5(2):233-236, 1996.Andrzej Trybulec. Tuples, projections and Cartesian products. Formalized Mathematics, 1(1):97-105, 1990.Andrzej Trybulec. On the sets inhabited by numbers. Formalized Mathematics, 11(4): 341-347, 2003.Andrzej Trybulec. Moore-Smith convergence. Formalized Mathematics, 6(2):213-225, 1997.Andrzej Trybulec and Agata Darmochwał. Boolean domains. Formalized Mathematics, 1 (1):187-190, 1990.Michał J. Trybulec. Integers. Formalized Mathematics, 1(3):501-505, 1990.Wojciech A. Trybulec and Grzegorz Bancerek. Kuratowski - Zorn lemma. Formalized Mathematics, 1(2):387-393, 1990.Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990.Tetsuya Tsunetou, Grzegorz Bancerek, and Yatsuka Nakamura. Zero-based finite sequences. Formalized Mathematics, 9(4):825-829, 2001.Josef Urban. Basic facts about inaccessible and measurable cardinals. Formalized Mathematics, 9(2):323-329, 2001.Claude Wagschal. Topologie et analyse fonctionnelle. Hermann, 1995.Edmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1 (1):73-83, 1990.Edmund Woronowicz. Relations defined on sets. Formalized Mathematics, 1(1):181-186, 1990.Stanisław Zukowski. Introduction to lattice theory. Formalized Mathematics, 1(1):215-222, 1990
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