Journal of Formalized Mathematics
Volume 13, 2001
University of Bialystok
Copyright (c) 2001
Association of Mizar Users
Compactness of Lim-inf Topology
-
Grzegorz Bancerek
-
University of Bialystok
-
Noboru Endou
-
Shinshu University, Nagano
Summary.
-
Formalization of [14], chapter III, section 3 (3.4-3.6).
The terminology and notation used in this paper have been
introduced in the following articles
[22]
[11]
[27]
[23]
[26]
[13]
[28]
[29]
[9]
[10]
[18]
[19]
[16]
[1]
[2]
[20]
[3]
[15]
[24]
[30]
[4]
[17]
[25]
[12]
[8]
[5]
[6]
[21]
[7]
Contents (PDF format)
Bibliography
- [1]
Grzegorz Bancerek.
Complete lattices.
Journal of Formalized Mathematics,
4, 1992.
- [2]
Grzegorz Bancerek.
Bounds in posets and relational substructures.
Journal of Formalized Mathematics,
8, 1996.
- [3]
Grzegorz Bancerek.
Directed sets, nets, ideals, filters, and maps.
Journal of Formalized Mathematics,
8, 1996.
- [4]
Grzegorz Bancerek.
Prime ideals and filters.
Journal of Formalized Mathematics,
8, 1996.
- [5]
Grzegorz Bancerek.
Bases and refinements of topologies.
Journal of Formalized Mathematics,
10, 1998.
- [6]
Grzegorz Bancerek.
The Lawson topology.
Journal of Formalized Mathematics,
10, 1998.
- [7]
Grzegorz Bancerek, Noboru Endou, and Yuji Sakai.
On the characterizations of compactness.
Journal of Formalized Mathematics,
13, 2001.
- [8]
Jozef Bialas and Yatsuka Nakamura.
Dyadic numbers and T$_4$ topological spaces.
Journal of Formalized Mathematics,
7, 1995.
- [9]
Czeslaw Bylinski.
Functions and their basic properties.
Journal of Formalized Mathematics,
1, 1989.
- [10]
Czeslaw Bylinski.
Functions from a set to a set.
Journal of Formalized Mathematics,
1, 1989.
- [11]
Czeslaw Bylinski.
Some basic properties of sets.
Journal of Formalized Mathematics,
1, 1989.
- [12]
Agata Darmochwal.
Compact spaces.
Journal of Formalized Mathematics,
1, 1989.
- [13]
Agata Darmochwal.
Finite sets.
Journal of Formalized Mathematics,
1, 1989.
- [14]
G. Gierz, K.H. Hofmann, K. Keimel, J.D. Lawson, M. Mislove, and D.S. Scott.
\em A Compendium of Continuous Lattices.
Springer-Verlag, Berlin, Heidelberg, New York, 1980.
- [15]
Adam Grabowski and Robert Milewski.
Boolean posets, posets under inclusion and products of relational structures.
Journal of Formalized Mathematics,
8, 1996.
- [16]
Zbigniew Karno.
Maximal discrete subspaces of almost discrete topological spaces.
Journal of Formalized Mathematics,
5, 1993.
- [17]
Artur Kornilowicz.
On the topological properties of meet-continuous lattices.
Journal of Formalized Mathematics,
8, 1996.
- [18]
Beata Padlewska.
Families of sets.
Journal of Formalized Mathematics,
1, 1989.
- [19]
Beata Padlewska and Agata Darmochwal.
Topological spaces and continuous functions.
Journal of Formalized Mathematics,
1, 1989.
- [20]
Alexander Yu. Shibakov and Andrzej Trybulec.
The Cantor set.
Journal of Formalized Mathematics,
7, 1995.
- [21]
Bartlomiej Skorulski.
Lim-inf convergence.
Journal of Formalized Mathematics,
12, 2000.
- [22]
Andrzej Trybulec.
Tarski Grothendieck set theory.
Journal of Formalized Mathematics,
Axiomatics, 1989.
- [23]
Andrzej Trybulec.
Tuples, projections and Cartesian products.
Journal of Formalized Mathematics,
1, 1989.
- [24]
Andrzej Trybulec.
Moore-Smith convergence.
Journal of Formalized Mathematics,
8, 1996.
- [25]
Andrzej Trybulec.
Scott topology.
Journal of Formalized Mathematics,
9, 1997.
- [26]
Wojciech A. Trybulec.
Partially ordered sets.
Journal of Formalized Mathematics,
1, 1989.
- [27]
Zinaida Trybulec.
Properties of subsets.
Journal of Formalized Mathematics,
1, 1989.
- [28]
Edmund Woronowicz.
Relations and their basic properties.
Journal of Formalized Mathematics,
1, 1989.
- [29]
Edmund Woronowicz.
Relations defined on sets.
Journal of Formalized Mathematics,
1, 1989.
- [30]
Mariusz Zynel and Czeslaw Bylinski.
Properties of relational structures, posets, lattices and maps.
Journal of Formalized Mathematics,
8, 1996.
Received July 29, 2001
[
Download a postscript version,
MML identifier index,
Mizar home page]