Convergent Filter Bases

Open access

Abstract

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).

If the inline PDF is not rendering correctly, you can download the PDF file here.

  • [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.

  • [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.

Search
Journal information
Impact Factor


CiteScore 2018: 0.42

SCImago Journal Rank (SJR) 2018: 0.111
Source Normalized Impact per Paper (SNIP) 2018: 0.169

Target audience:

researchers in the fields of formal methods and computer-checked mathematics

Cited By
Metrics
All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 161 63 0
PDF Downloads 72 44 0