Various convergences of multifunctions. (English) Zbl 1497.54020
Summary: In the present paper, we introduce different types of convergences of nets of multifunctions from one topological space to another and compare them. Attempt has been made to formulate sufficient conditions under which these convergences preserve slight \(B^\ast\)-continuity of the limit multifunction.
MSC:
54C60 | Set-valued maps in general topology |
54A20 | Convergence in general topology (sequences, filters, limits, convergence spaces, nets, etc.) |
54C08 | Weak and generalized continuity |
54C10 | Special maps on topological spaces (open, closed, perfect, etc.) |
54D20 | Noncompact covering properties (paracompact, Lindelöf, etc.) |
40A30 | Convergence and divergence of series and sequences of functions |
Keywords:
\(\tau_{cl}^+\)-pointwise convergence; \(\tau_{cl}^-\)-pointwise convergence; \(cl\)-convergence; nearly-strong convergernceReferences:
[1] | R. F. Arens, A topology for spaces of transformations.Ann. of Math. (2)47(1946), 480-495. · Zbl 0060.39704 |
[2] | I. Domnik, On strong convergence of multivalued maps.Math. Slovaca53(2003), no. 2, 199-209. · Zbl 1051.54017 |
[3] | D. K. Ganguly, P. Mallick, On generalized continuous multifunctions and their selections.Real Anal. Exchange33 (2008), no. 2, 449-456. · Zbl 1160.26001 |
[4] | D. K. Ganguly, P. Mallick, On convergence preserving generalized continuous multifunctions.Questions Answers Gen. Topology27(2009), no. 2, 125-132. · Zbl 1182.54004 |
[5] | D. K. Ganguly, C. Mitra, B∗-continuity and other generalised continuity.Rev. Acad. Canaria Cienc.12(2000), no. 1-2, 9-17 (2001). · Zbl 0986.54023 |
[6] | D. K. Ganguly, C. Mitra, On some weaker forms ofB∗-continuity for multifunction.Soochow J. Math.32(2006), no. 1, 59-69. · Zbl 1107.54013 |
[7] | P. Jain, C. Basu, V. Panwar, On generalizedB∗-continuity,B∗-coverings andB∗-separations.Eurasian Math. J. 10(2019), no. 3, 28-39. · Zbl 1463.54048 |
[8] | P. Jain, C. Basu, V. Panwar, OnB∗-clopen continuity, oscillation and convergence.Tbilisi Math. J.13(2020), no. 4, 129-140. · Zbl 1490.54016 |
[9] | P. Jain, C. Basu, V. Panwar,B∗-continuity for multifunctions based on clustering.Azerb. J. Math.2021, Special issue, 3-14. · Zbl 1473.54011 |
[10] | P. Jain, C. Basu, V. Panwar, Selection of slightlyB∗-continuous multifunctions.Eurasian Math. J.13(2022), 55-61. · Zbl 1513.54084 |
[11] | J. L. Kelley,General Topology. D. Van Nostrand Co., Inc., Toronto-New York-London, 1955. · Zbl 0066.16604 |
[12] | I. Kupka, V. Toma, A uniform convergence for non-uniform spaces.Publ. Math. Debrecen47(1995), no. 3-4, 299-309. · Zbl 0879.54003 |
[13] | M. Matejdes, Sur les s´electeurs des multifonctions. (French)Math. Slovaca37(1987), no. 1, 111-124. · Zbl 0629.54013 |
[14] | M. Matejdes, Selection theorems and minimal mappings in a cluster setting.Rocky Mountain J. Math.41(2011), no. 3, 851-867. · Zbl 1234.54027 |
[15] | T. Neubrunn, Quasi continuity.Real. Anal. Exch.14(1998-99), 258-308. |
[16] | T. Noiri, V. Popa, Slightlym-continuous multifunctions.Bull. Inst. Math. Acad. Sin. (N.S.)1(2006), no. 4 · Zbl 1114.54009 |
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