On the Baire Category Theorem

Journal of Formalized Mathematics
Volume 9, 1997
University of Bialystok
Copyright (c) 1997 Association of Mizar Users

On the Baire Category Theorem

Artur Kornilowicz: Warsaw University, Bialystok

Summary.

In this paper Exercise 3.43 from Chapter 1 of [14] is solved.

This work has been partially supported by the Office of Naval Research Grant N00014-95-1-1336.

MML Identifier: WAYBEL12

The terminology and notation used in this paper have been introduced in the following articles [21] [11] [25] [23] [26] [9] [10] [7] [13] [8] [1] [2] [19] [24] [27] [12] [16] [20] [3] [4] [15] [5] [28] [17] [6] [18] [22]

Contents (PDF format)

Preliminaries
On the Baire Category Theorem

Bibliography

[1] Grzegorz Bancerek. Cardinal numbers. Journal of Formalized Mathematics, 1, 1989.

[2] Grzegorz Bancerek. Countable sets and Hessenberg's theorem. Journal of Formalized Mathematics, 2, 1990.

[3] Grzegorz Bancerek. Complete lattices. Journal of Formalized Mathematics, 4, 1992.

[4] Grzegorz Bancerek. Bounds in posets and relational substructures. Journal of Formalized Mathematics, 8, 1996.

[5] Grzegorz Bancerek. Directed sets, nets, ideals, filters, and maps. Journal of Formalized Mathematics, 8, 1996.

[6] Grzegorz Bancerek. The ``way-below'' relation. Journal of Formalized Mathematics, 8, 1996.

[7] Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Journal of Formalized Mathematics, 1, 1989.

[8] Jozef Bialas. Group and field definitions. Journal of Formalized Mathematics, 1, 1989.

[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. Families of subsets, subspaces and mappings in topological 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. Remarks on special subsets of topological spaces. Journal of Formalized Mathematics, 5, 1993.

[17] Artur Kornilowicz. Definitions and properties of the join and meet of subsets. Journal of Formalized Mathematics, 8, 1996.

[18] Beata Madras. Irreducible and prime elements. Journal of Formalized Mathematics, 8, 1996.

[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] Andrzej Trybulec. Tarski Grothendieck set theory. Journal of Formalized Mathematics, Axiomatics, 1989.

[22] Andrzej Trybulec. Baire spaces, Sober spaces. Journal of Formalized Mathematics, 9, 1997.

[23] Andrzej Trybulec. Subsets of real numbers. Journal of Formalized Mathematics, Addenda, 2003.

[24] Wojciech A. Trybulec. Partially ordered sets. Journal of Formalized Mathematics, 1, 1989.

[25] Zinaida Trybulec. Properties of subsets. Journal of Formalized Mathematics, 1, 1989.

[26] Edmund Woronowicz. Relations and their basic properties. Journal of Formalized Mathematics, 1, 1989.

[27] Miroslaw Wysocki and Agata Darmochwal. Subsets of topological spaces. Journal of Formalized Mathematics, 1, 1989.

[28] Mariusz Zynel and Czeslaw Bylinski. Properties of relational structures, posets, lattices and maps. Journal of Formalized Mathematics, 8, 1996.

Received February 5, 1997

[ Download a postscript version, MML identifier index, Mizar home page]