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Tytuł artykułu

Convergent Filter Bases

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We 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).
Słowa kluczowe
Wydawca
Rocznik
Tom
23
Numer
3
Strony
189-203
Opis fizyczny
Daty
wydano
2015-09-01
otrzymano
2015-06-30
online
2015-09-30
Twórcy
  • Rue de la Brasserie 5 7100 La Louvière, Belgium
Bibliografia
  • [1] Grzegorz Bancerek. Cardinal numbers. Formalized Mathematics, 1(2):377-382, 1990.
  • [2] Grzegorz Bancerek. König’s theorem. Formalized Mathematics, 1(3):589-593, 1990.
  • [3] Grzegorz Bancerek. Complete lattices. Formalized Mathematics, 2(5):719-725, 1991.
  • [4] Grzegorz Bancerek. The fundamental properties of natural numbers. Formalized Mathematics, 1(1):41-46, 1990.
  • [5] Grzegorz Bancerek. The ordinal numbers. Formalized Mathematics, 1(1):91-96, 1990.
  • [6] Grzegorz Bancerek. Directed sets, nets, ideals, filters, and maps. Formalized Mathematics, 6(1):93-107, 1997.
  • [7] Grzegorz Bancerek. Prime ideals and filters. Formalized Mathematics, 6(2):241-247, 1997.
  • [8] Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Formalized Mathematics, 1(1):107-114, 1990.
  • [9] Grzegorz Bancerek, Noboru Endou, and Yuji Sakai. On the characterizations of compactness. Formalized Mathematics, 9(4):733-738, 2001.
  • [10] Nicolas Bourbaki. General Topology: Chapters 1-4. Springer Science and Business Media, 2013.
  • [11] Czesław Bylinski. Functions and their basic properties. Formalized Mathematics, 1(1): 55-65, 1990.
  • [12] Czesław Bylinski. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990.
  • [13] Czesław Bylinski. Basic functions and operations on functions. Formalized Mathematics, 1(1):245-254, 1990.
  • [14] Czesław Bylinski. Partial functions. Formalized Mathematics, 1(2):357-367, 1990.
  • [15] Czesław Bylinski. Some basic properties of sets. Formalized Mathematics, 1(1):47-53, 1990.
  • [16] Henri Cartan. Théorie des filtres. C. R. Acad. Sci., CCV:595-598, 1937.
  • [17] Marek Chmur. The lattice of natural numbers and the sublattice of it. The set of prime numbers. Formalized Mathematics, 2(4):453-459, 1991.
  • [18] Agata Darmochwał. Finite sets. Formalized Mathematics, 1(1):165-167, 1990.
  • [19] Adam Grabowski and Robert Milewski. Boolean posets, posets under inclusion and products of relational structures. Formalized Mathematics, 6(1):117-121, 1997.
  • [20] Gilbert Lee and Piotr Rudnicki. Dickson’s lemma. Formalized Mathematics, 10(1):29-37, 2002.
  • [21] 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]
  • [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] Alexander Yu. Shibakov and Andrzej Trybulec. The Cantor set. Formalized Mathematics, 5(2):233-236, 1996.
  • [25] Andrzej Trybulec. Tuples, projections and Cartesian products. Formalized Mathematics, 1(1):97-105, 1990.
  • [26] Andrzej Trybulec. On the sets inhabited by numbers. Formalized Mathematics, 11(4): 341-347, 2003.
  • [27] Andrzej Trybulec. Moore-Smith convergence. Formalized Mathematics, 6(2):213-225, 1997.
  • [28] Andrzej Trybulec and Agata Darmochwał. Boolean domains. Formalized Mathematics, 1 (1):187-190, 1990.
  • [29] Michał J. Trybulec. Integers. Formalized Mathematics, 1(3):501-505, 1990.
  • [30] Wojciech A. Trybulec and Grzegorz Bancerek. Kuratowski - Zorn lemma. Formalized Mathematics, 1(2):387-393, 1990.
  • [31] Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990.
  • [32] Tetsuya Tsunetou, Grzegorz Bancerek, and Yatsuka Nakamura. Zero-based finite sequences. Formalized Mathematics, 9(4):825-829, 2001.
  • [33] Josef Urban. Basic facts about inaccessible and measurable cardinals. Formalized Mathematics, 9(2):323-329, 2001.
  • [34] Claude Wagschal. Topologie et analyse fonctionnelle. Hermann, 1995.
  • [35] Edmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1 (1):73-83, 1990.
  • [36] Edmund Woronowicz. Relations defined on sets. Formalized Mathematics, 1(1):181-186, 1990.
  • [37] Stanisław Zukowski. Introduction to lattice theory. Formalized Mathematics, 1(1):215-222, 1990.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_1515_forma-2015-0016
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