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

Baire Spaces, Sober Spaces


Andrzej Trybulec
Warsaw University, Bialystok

Summary.

In the article concepts and facts necessary to continue formalization of theory of continuous lattices according to [11] are introduced.

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

MML Identifier: YELLOW_8

The terminology and notation used in this paper have been introduced in the following articles [16] [8] [18] [19] [7] [15] [13] [2] [1] [3] [5] [10] [17] [14] [20] [12] [6] [9] [4]

Contents (PDF format)

  1. Preliminaries
  2. Families of complements
  3. Topological preliminaries
  4. Baire Spaces
  5. Sober Spaces
  6. More on regular spaces

Bibliography

[1] Grzegorz Bancerek. Cardinal numbers. Journal of Formalized Mathematics, 1, 1989.
[2] Grzegorz Bancerek. Zermelo theorem and axiom of choice. Journal of Formalized Mathematics, 1, 1989.
[3] Grzegorz Bancerek. Countable sets and Hessenberg's theorem. Journal of Formalized Mathematics, 2, 1990.
[4] Grzegorz Bancerek. The ``way-below'' relation. Journal of Formalized Mathematics, 8, 1996.
[5] Jozef Bialas. Group and field definitions. Journal of Formalized Mathematics, 1, 1989.
[6] Jozef Bialas and Yatsuka Nakamura. Dyadic numbers and T$_4$ topological spaces. Journal of Formalized Mathematics, 7, 1995.
[7] Czeslaw Bylinski. Functions and their basic properties. Journal of Formalized Mathematics, 1, 1989.
[8] Czeslaw Bylinski. Some basic properties of sets. Journal of Formalized Mathematics, 1, 1989.
[9] Agata Darmochwal. Compact spaces. Journal of Formalized Mathematics, 1, 1989.
[10] Agata Darmochwal. Finite sets. Journal of Formalized Mathematics, 1, 1989.
[11] 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.
[12] Zbigniew Karno. Remarks on special subsets of topological spaces. Journal of Formalized Mathematics, 5, 1993.
[13] Beata Padlewska. Families of sets. Journal of Formalized Mathematics, 1, 1989.
[14] Beata Padlewska and Agata Darmochwal. Topological spaces and continuous functions. Journal of Formalized Mathematics, 1, 1989.
[15] Alexander Yu. Shibakov and Andrzej Trybulec. The Cantor set. Journal of Formalized Mathematics, 7, 1995.
[16] Andrzej Trybulec. Tarski Grothendieck set theory. Journal of Formalized Mathematics, Axiomatics, 1989.
[17] Andrzej Trybulec and Agata Darmochwal. Boolean domains. Journal of Formalized Mathematics, 1, 1989.
[18] Zinaida Trybulec. Properties of subsets. Journal of Formalized Mathematics, 1, 1989.
[19] Edmund Woronowicz. Relations and their basic properties. Journal of Formalized Mathematics, 1, 1989.
[20] Miroslaw Wysocki and Agata Darmochwal. Subsets of topological spaces. Journal of Formalized Mathematics, 1, 1989.

Received January 8, 1997

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