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

Scott-Continuous Functions


Adam Grabowski
University of Bialystok

Summary.

The article is a translation of [10, pp. 112-113].

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

MML Identifier: WAYBEL17

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

Contents (PDF format)

  1. Preliminaries
  2. Poset of Continuous Maps
  3. Some Special Nets
  4. Monotone Maps
  5. Necessary and Sufficient Conditions of Scott-continuity

Bibliography

[1] Grzegorz Bancerek. The fundamental properties of natural numbers. Journal of Formalized Mathematics, 1, 1989.
[2] Grzegorz Bancerek. Complete lattices. Journal of Formalized Mathematics, 4, 1992.
[3] Grzegorz Bancerek. Bounds in posets and relational substructures. Journal of Formalized Mathematics, 8, 1996.
[4] Grzegorz Bancerek. Directed sets, nets, ideals, filters, and maps. Journal of Formalized Mathematics, 8, 1996.
[5] Grzegorz Bancerek. The ``way-below'' relation. Journal of Formalized Mathematics, 8, 1996.
[6] Czeslaw Bylinski. Functions and their basic properties. Journal of Formalized Mathematics, 1, 1989.
[7] Czeslaw Bylinski. Functions from a set to a set. 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] 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.
[11] Adam Grabowski. On the category of posets. Journal of Formalized Mathematics, 8, 1996.
[12] Adam Grabowski and Robert Milewski. Boolean posets, posets under inclusion and products of relational structures. Journal of Formalized Mathematics, 8, 1996.
[13] Krzysztof Hryniewiecki. Relations of tolerance. Journal of Formalized Mathematics, 2, 1990.
[14] Artur Kornilowicz. Meet -- continuous lattices. Journal of Formalized Mathematics, 8, 1996.
[15] Artur Kornilowicz. On the topological properties of meet-continuous lattices. Journal of Formalized Mathematics, 8, 1996.
[16] Robert Milewski. Algebraic lattices. Journal of Formalized Mathematics, 8, 1996.
[17] Beata Padlewska and Agata Darmochwal. Topological spaces and continuous functions. Journal of Formalized Mathematics, 1, 1989.
[18] Andrzej Trybulec. Tarski Grothendieck set theory. Journal of Formalized Mathematics, Axiomatics, 1989.
[19] Andrzej Trybulec. Natural transformations. Discrete categories. Journal of Formalized Mathematics, 3, 1991.
[20] Andrzej Trybulec. Scott topology. Journal of Formalized Mathematics, 9, 1997.
[21] Andrzej Trybulec. Subsets of real numbers. Journal of Formalized Mathematics, Addenda, 2003.
[22] Wojciech A. Trybulec. Partially ordered sets. Journal of Formalized Mathematics, 1, 1989.
[23] Zinaida Trybulec. Properties of subsets. Journal of Formalized Mathematics, 1, 1989.
[24] Edmund Woronowicz. Relations and their basic properties. Journal of Formalized Mathematics, 1, 1989.
[25] Edmund Woronowicz. Relations defined on sets. Journal of Formalized Mathematics, 1, 1989.
[26] Mariusz Zynel and Czeslaw Bylinski. Properties of relational structures, posets, lattices and maps. Journal of Formalized Mathematics, 8, 1996.

Received February 13, 1998

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