A Note on the Set of Discontinuity Points of Multifunctions of two Variables

Grażyna Kwiecińka

doi:10.2478/tmmp-2014-0013

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A Note on the Set of Discontinuity Points of Multifunctions of two Variables

Tatra Mountains Mathematical Publications

Volume 58 (2014): Issue 1 (March 2014)

By: Grażyna Kwiecińka

Open Access

|Aug 2014

Abstract

In this paper, we consider some problem connected with separate properties of a multifunction of two variables which ensure that the set of its joint discontinuity points is a meager set.

References

[1] BAIRE, R.: Sur les fonctions des variables reelles, Ann. Mat. Appl. 3 (1899), 1-22.10.1007/BF02419243
Search in Google Scholar
[2] BRISAC, R.: Les classes de Baire des fonctions multiformes, C. R. Acad. Sci. Paris 224 (1974), 257-258.
Search in Google Scholar
[3] EWERT, J.: Multivalued mappings and bitopological spaces. SŁupsk, 1985. (In Polish)
Search in Google Scholar
[4] FUDALI, L. A.: On cliquish functions on product spaces, Math. Slovaca 33 (1988), 53-58.
Search in Google Scholar
[5] GARG, K. M.: On the classification of set-valued functions, Real Anal. Exchange 9 (1983-1984), 86-93.10.2307/44153516
Search in Google Scholar
[6] GRANDE, Z.: On functions of two variables equicontinuous in one variable, Real Anal. Exchange 22 (1996-97), 760-765.10.2307/44153952
Search in Google Scholar
[7] HANSEL, R.W.: Hereditarily additive families in descriptive set theory and measurable multimaps, Trans. Amer. Math. Soc. 278 (1983), 725-749.
Search in Google Scholar
[8] HENRIKSEN, H.-WOODS, R. G.: Separate versus joint continuity: A tale of four topologies, Topology Appl. 97 (1999), 175-205.10.1016/S0166-8641(98)00076-5
Search in Google Scholar
[9] HOLá, L’.-PIOTROWSKI, Z.: Set of continuity points of functions with values in generalized metric spaces, Tatra Mt. Math. Publ. 42 (2009), 1-12.
Search in Google Scholar
[10] KEMPISTY, S.: Sur les fonctions semi-continues par raport á chacume de deux variables, Fund. Math. 14 (1929), 237-241.10.4064/fm-14-1-237-241
Search in Google Scholar
[11] KERSHNER, R.: The continuity of functions of many variables, Trans. Amer. Math. Soc. 53 (1943), 83-100.10.1090/S0002-9947-1943-0007522-5
Search in Google Scholar
[12] KLEIN, E.-THOMPSON, A. C.: Theory of Correspondences, in: Canad. Math. Soc. Ser. Monographs Adv. Texts, A Wiley-Interscience Publication. John Wiley & Sons, Inc., New York, 1984
Search in Google Scholar
[13] KURATOWSKI, K.: On set-valued B-measurable mappings and a theorem of Hausdorff, in: Theory Sets Topology, Collection Papers Honour Felix Hausdorff, Berlin, 1972, pp. 355-362.
Search in Google Scholar
[14] KWIECIŃSKA, G.: On the Borel class of multivalued functions of two variables, Topology Proc. 25 (2000), 601-613.
Search in Google Scholar
[15] MATEJDES, M.: Continuity of multifunctions, Real Anal. Exchange 19 (1992-1993), 394-413.10.2307/44152391
Search in Google Scholar
[16] NEUBRUNN, T.: Quasi-continuity, Real Anal. Exchange 14 (1988-89), 259-305.10.2307/44151947
Search in Google Scholar
[17] PIOTROWSKI, Z.: The genesis of separate versus joint continuity, Tatra Mt. Math. Publ. 8 (1996), 113-126.
Search in Google Scholar

Articles in this issue

DOI: https://doi.org/10.2478/tmmp-2014-0013 | Journal eISSN: 1338-9750 | Journal ISSN: 1210-3195

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Language: English

Page range: 145 - 154

Submitted on: Jan 2, 2014

Published on: Aug 15, 2014

Published by: Slovak Academy of Sciences, Mathematical Institute

In partnership with: Paradigm Publishing Services

Publication frequency: 1 issue per year

Keywords:

multifunctions,

semicontinuity of a multifunction,

lower and upper Baire classes of multifunctions

Related subjects:

Mathematics,

General mathematics

© 2014 Grażyna Kwiecińka, published by Slovak Academy of Sciences, Mathematical Institute
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Volume 58 (2014): Issue 1 (March 2014)