On single-valued and multi-valued convergences

• Autorzy: Bacher, Ł. , Kamiński, A. , Nalepa, R.
• Konferencja: Informatics and Related Fields / XIV International Conference on Mathematics (XIV ; 7-11.11.2008 ; Ustrzyki Dolne, Polska)
• Języki publikacji: EN

Abstrakty

EN

We present a review of ideas of a general theory of convergence, developed independently of topology, with the stress on the duality of convergence and topology. Results and problems concerning sufficient and necessary conditions for a convergence to be topological, both in case of the single- and multi-valued cases, are recalled. We reconstruct, filling certain gaps, an example given in [7] to show that one of sufficient conditions in the theorems proved in [1] and [9] for multi-valued convergences to be topological is not necessary.

Słowa kluczowe

PL

zbieżność jednowartościowa; zbieżność wielowartościowa; koneksja Galois; teoria Galois

EN

L-Frechet space; single-valued convergence; multi-valued convergence; topological convergence; Galois connection

• Czasopismo: Journal of Mathematics and Applications
• Rocznik: 2009
• Tom: Vol. 31
• Strony: 19-27
• Opis fizyczny: Bibliogr. 16 poz.

Twórcy

autor

Bacher, Ł.

autor

Kamiński, A.

autor

Nalepa, R.

• Institute of Mathematics University of Rzeszów Rejtana 16A, 35-510 Rzeszów,

Bibliografia

• [1] P. Antosik, On topology of convergence, Colloq. Math. 21 (1970), pp. 205-209.
• [2] L. Bacher, A. Kamiński, R. Nalepa, On Kisyński's theorem and multi-valued convergences, to appear.
• [3] A.R. Bednarek, J. Mikusi´nski, Convergence and topology, Bull. Pol. Acad. Sci.Math. 17 (1969), pp. 437-442.
• [4] G. Birkhoff, Lattice Theory, Providence, 1961.
• [5] M. Dolcher, Topologie e strutture di convergenza, Ann. Sc. Norm. Super. Pisa, Cl. Sci. (3) 14 (1960), pp. 63-92.
• [6] R. Engelking, General Topology, PWN, Warsaw 1977.
• [7] C. Ferens, A. Kamiński, C. Kliś, Some examples of topological and non-topological convergences, in: Proc. Conf. on Convergence, Szczyrk 1979, PAN, Katowice 1980, pp. 17-23.
• [8] M. Frechet, Sur la notion de voisinage les ensembles abstraits, Bull. Sci. Math. 42 (1918), pp. 138-156.
• [9] A. Kamiński, On Antosik's theorem concerning topological convergence, in: Proc. Conf. on Convergence, Szczyrk 1979, PAN, Katowice 1980, pp. 46-49.
• [10] A. Kamiński, On characterization of topological convergence, in: Proc. Conf. on Convergence, Szczyrk 1979, PAN, Katowice 1980, pp. 50-70.
• [11] A. Kamiński, On multivalued topological convergences, Bull. Pol. Acad. Sci.Math. 29 (1981), pp. 605-608.
• [12] A. Kamiński, Remarks on multivalued convergences, in: General Topology and its Relations to Modern Analysis and Algebra V, Proc. Fifth Prague Top. Symp. 1981 (ed. J. Novak), Heldermann, Berlin 1983, pp. 418-422.
• [13] J. Kisyński, Convergence du type L, Colloq. Math. 7 (1960), pp. 205-211.
• [14] J. Mikusiński, Operational Calculus, Vol. I., PWN - Pergamon Press, 1987.
• [15] J. Novak, On some problems concerning multivalued convergences, Czechoslovak Math. J. 14 (1964), pp. 548-561.
• [16] P. Urysohn, Sur les classes (L) de M. Fr´echet, Enseign. Math. 25 (1926), pp.77-83.