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

Bases and Refinements of Topologies


Grzegorz Bancerek
University of Bialystok

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

MML Identifier: YELLOW_9

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

Contents (PDF format)

  1. Subsets as Nets
  2. Operations on Families of Open Sets
  3. Bases
  4. Product Topologies
  5. Topological Augmentations
  6. Refinements

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] Jozef Bialas. Group and field definitions. Journal of Formalized Mathematics, 1, 1989.
[5] Czeslaw Bylinski. Functions and their basic properties. Journal of Formalized Mathematics, 1, 1989.
[6] Czeslaw Bylinski. Functions from a set to a set. Journal of Formalized Mathematics, 1, 1989.
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[13] Beata Padlewska and Agata Darmochwal. Topological spaces and continuous functions. Journal of Formalized Mathematics, 1, 1989.
[14] Alexander Yu. Shibakov and Andrzej Trybulec. The Cantor set. Journal of Formalized Mathematics, 7, 1995.
[15] Andrzej Trybulec. Tarski Grothendieck set theory. Journal of Formalized Mathematics, Axiomatics, 1989.
[16] Andrzej Trybulec. Tuples, projections and Cartesian products. Journal of Formalized Mathematics, 1, 1989.
[17] Andrzej Trybulec. A Borsuk theorem on homotopy types. Journal of Formalized Mathematics, 3, 1991.
[18] Andrzej Trybulec. Moore-Smith convergence. Journal of Formalized Mathematics, 8, 1996.
[19] Andrzej Trybulec. Scott topology. Journal of Formalized Mathematics, 9, 1997.
[20] Wojciech A. Trybulec. Partially ordered sets. Journal of Formalized Mathematics, 1, 1989.
[21] Zinaida Trybulec. Properties of subsets. Journal of Formalized Mathematics, 1, 1989.
[22] Edmund Woronowicz. Relations and their basic properties. Journal of Formalized Mathematics, 1, 1989.
[23] Edmund Woronowicz. Relations defined on sets. Journal of Formalized Mathematics, 1, 1989.
[24] Edmund Woronowicz and Anna Zalewska. Properties of binary relations. Journal of Formalized Mathematics, 1, 1989.

Received March 9, 1998


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