On the Characterization of Hausdorff Spaces

Journal of Formalized Mathematics
Volume 10, 1998
University of Bialystok
Copyright (c) 1998 Association of Mizar Users

On the Characterization of Hausdorff Spaces

Artur Kornilowicz: University of Bialystok

This work has been supported by KBN Grant 8 T11C 018 12.

MML Identifier: YELLOW12

The terminology and notation used in this paper have been introduced in the following articles [18] [9] [25] [14] [26] [7] [27] [8] [19] [6] [16] [10] [17] [15] [20] [28] [24] [1] [2] [3] [11] [12] [13] [4] [21] [22] [23] [5]

Contents (PDF format)

The Properties of Some Functions
The Properties of the Relational Structures
On the Hausdorff Spaces

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. The ``way-below'' relation. Journal of Formalized Mathematics, 8, 1996.

[5] Grzegorz Bancerek. Bases and refinements of topologies. Journal of Formalized Mathematics, 10, 1998.

[6] Czeslaw Bylinski. Basic functions and operations on functions. Journal of Formalized Mathematics, 1, 1989.

[7] Czeslaw Bylinski. Functions and their basic properties. Journal of Formalized Mathematics, 1, 1989.

[8] Czeslaw Bylinski. Partial functions. Journal of Formalized Mathematics, 1, 1989.

[9] Czeslaw Bylinski. Some basic properties of sets. Journal of Formalized Mathematics, 1, 1989.

[10] Agata Darmochwal. Families of subsets, subspaces and mappings in topological spaces. Journal of Formalized Mathematics, 1, 1989.

[11] Artur Kornilowicz. Cartesian products of relations and relational structures. Journal of Formalized Mathematics, 8, 1996.

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

[13] Artur Kornilowicz. Meet -- continuous lattices. Journal of Formalized Mathematics, 8, 1996.

[14] Beata Padlewska. Families of sets. Journal of Formalized Mathematics, 1, 1989.

[15] Beata Padlewska. Locally connected spaces. Journal of Formalized Mathematics, 2, 1990.

[16] Beata Padlewska and Agata Darmochwal. Topological spaces and continuous functions. Journal of Formalized Mathematics, 1, 1989.

[17] Alexander Yu. Shibakov and Andrzej Trybulec. The Cantor set. Journal of Formalized Mathematics, 7, 1995.

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

[19] Andrzej Trybulec. Tuples, projections and Cartesian products. Journal of Formalized Mathematics, 1, 1989.

[20] Andrzej Trybulec. A Borsuk theorem on homotopy types. Journal of Formalized Mathematics, 3, 1991.

[21] Andrzej Trybulec. Moore-Smith convergence. Journal of Formalized Mathematics, 8, 1996.

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

[23] Andrzej Trybulec. Scott topology. Journal of Formalized Mathematics, 9, 1997.

[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] Edmund Woronowicz. Relations defined on sets. Journal of Formalized Mathematics, 1, 1989.

[28] Mariusz Zynel and Adam Guzowski. \Tzero\ topological spaces. Journal of Formalized Mathematics, 6, 1994.

Received April 18, 1998

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