Moore-Smith Convergence

Andrzej Trybulec

Warsaw University, Bialystok

Summary.

The paper introduces the concept of a net (a generalized sequence). The goal is to enable the continuation of the translation of [14].

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

MML Identifier: YELLOW_6

Contents (PDF format)

1. Preliminaries
2. Topological spaces
3. 1-sorted structures
4. Relational structures
5. Substructures of nets
6. More about nets
7. The restriction of a net
8. The universe of nets
9. Parametrized families of nets, iteration
10. Poset of open neighbourhoods
11. Nets in topological spaces
12. Convergence classes

Bibliography

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

[2] Grzegorz Bancerek. The ordinal numbers. Journal of Formalized Mathematics, 1, 1989.

[3] Grzegorz Bancerek. K\"onig's theorem. Journal of Formalized Mathematics, 2, 1990.

[4] Grzegorz Bancerek. Tarski's classes and ranks. Journal of Formalized Mathematics, 2, 1990.

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

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

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

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

[9] Czeslaw Bylinski. Binary operations. Journal of Formalized Mathematics, 1, 1989.

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

[11] Czeslaw Bylinski. Functions from a set to a set. Journal of Formalized Mathematics, 1, 1989.

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

[13] Agata Darmochwal. Compact spaces. 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] Artur Kornilowicz. Cartesian products of relations and relational structures. Journal of Formalized Mathematics, 8, 1996.

[17] Jaroslaw Kotowicz. Monotone real sequences. Subsequences. Journal of Formalized Mathematics, 1, 1989.

[18] Beata Madras. Product of family of universal algebras. Journal of Formalized Mathematics, 5, 1993.

[19] Yatsuka Nakamura, Piotr Rudnicki, Andrzej Trybulec, and Pauline N. Kawamoto. Preliminaries to circuits, I. Journal of Formalized Mathematics, 6, 1994.

[20] Bogdan Nowak and Grzegorz Bancerek. Universal classes. Journal of Formalized Mathematics, 2, 1990.

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

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

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

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

[25] Andrzej Trybulec. Many-sorted sets. Journal of Formalized Mathematics, 5, 1993.

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

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

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

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