Upper and lower cl-supercontinuous multifunctions

J.K. Kohli

India

University of Delhi

Dept.of Mathematics, Hindu College, University of Delhi, Delhi 110007, India.

C.P. Arya

India

University of Delhi

Dept.of Mathematics, University of Delhi, Delhi 110007, India.

Submitted: 2013-07-23

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Accepted: 2013-07-23

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Published: 2013-07-23

DOI: https://doi.org/10.4995/agt.2013.1608
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Keywords:

upper(lower)cl-supercontinuous multifunction, strongly continuous multifunction, upper(lower) perfectly continuous multifunction, upper(lower) z-supercontinuous multifunction, upper( lower) D-supercontinuous multifunction

Supporting agencies:

This research was not funded

Abstract:

The notion of cl-supercontinuity ( clopen continuity) of functions is extended to the realm of multifunctions. Basic properties of upper(lower) cl-supercontinuous multifunctions are studied and their place in the hierarchy of strong variants of continuity of multifunctions is discussed. Examples are included to reflect upon the distinctiveness of upper (lower) cl-supercontinuity of multifunctions from that of othe rstrong variants of continuity of multifunctions which already exist in the literature.
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References:

M. Akdag, On the upper and lower super D-continuous multifunctions, Instanbul Univ. Sciences Faculty, Journal of Mathehmatics 60 (2001), 101–109.

M. Akdag, On supercontinuous multifunctions, Acta Math. Hungar. 99, no. 1-2 (2003), 143–153. http://dx.doi.org/10.1023/A:1024565630572

M. Akdag, On upper and lower z-supercontinuous multifunctions, Kyungpook Math. J. 45 (2005), 221–230.

M. Akdag, On upper and lower D-supercontinuous multifunctions, Miskolc Mathematical Notes 7, no. 1 (2006), 3–11.

S. P. Arya and R. Gupta, On strongly continuous mappings, Kyungpook Math. J. 14 (1974),131–143.

L. Górniewicz, Topological fixed point Theory of Multivalued Mappings, Kluwer Academic Publishers, Dordrect, T [7] N. C. Heldermann, Developability and some new regularity axiom, Canad. J. Math.33 (1981), 641–663.

L’. Hola, V. Balaz and T. Neubrunn, Remarks on c-upper semicontinuous multifunctions, Acta Mat. Univ. Comenianae 50/51 (1987), 159–165.

L’. Hola, Some conditions that imply continuity of almost continuous multifunctions, Acta Mat. Univ. 52/53 (1987), 159–165.

L’. Hola, Remarks on almost continuous multifunctions, Math. Slovaca 38 (1988), 325–331.

J. L. Kelley, General Topology, Van Nastrand, New York 1955.

J. K. Kohli and C. P. Arya, Strongly continuous and perfectly continuous multifunctions, Sci. Stud. Res. Ser. Math. Inform. 20, no. 1 (2010), 103–117.

J. K. Kohli and R. Kumar, z-supercontinuous functions, Indian J. Pure Appl. Math. 33, no. 7 (2002), 1097–1108.

J. K. Kohli and A. K. Das, New normality axioms and decompositions of normality, Glasnik Mat. 37(57) (2002), 105–114.

J. K. Kohli and D. Singh, Function spaces and certain strong variants of continuity, Applied General Topology 9, no. 1 (2008), 33–38.

Y. Kucuk, On strongly -continuous multifunctions, Pure and Appl. Math. Sci. 40 (1994), 43–54.

N. Levine, Strong continuity in topological spaces, Amer. Math. Monthly, 67 (1960), 269. http://dx.doi.org/10.2307/2309695

J. Mack, Countable paracompactness and weak normality properties, Trans. Amer.Math. Soc. 148 (1970), 265–272. http://dx.doi.org/10.1090/S0002-9947-1970-0259856-3

T. Noiri, Supercontinuity and some strong forms of continuity, Indian J. Pure Appl. Math. 15, no. 3 (1984), 241–250.

I. L. Reilly and M. K. Vamanamurthy, On supercontinuous mappings, Indian J. Pure Appl. Math. 14, no. 6 (1983), 767–772.

D. Singh, cl-supercontinuous functions, Applied General Topology 8, no. 2 (2007), 293–300.

R. E. Smithson, Almost and weak continuity for multifunctions, Bull. Calcutta Math. Soc. 70 (1978), 383–390.

R. Staum, The algebra of bounded continuous functions into non Archimedean field, Pac. J. Math. 50, no. 1 (1974), 169–185. http://dx.doi.org/10.2140/pjm.1974.50.169

A. Sostak, On a class of topological spaces containing all bicompact and connected spaces, General topology and its relation to modern analysis and algebra IV: Proceedings of the 4th Prague topological symposium, (1976) part B 445-451.

N.V. Velicko, H-closed topological spaces, Amer. Math. Soc. Transl. 78, no. 2 (1968), 103–118.

G. T. Whyburn, Continuity of Multifunctions, Proc. N. A. S. 54 (1965), 1494–1501.

I. Zorlutuna and Y. Kucuk, Super and strongly faintly continuous multifunctions, Applied Math. E-Notes 1 (2001), 47–55.he Netherlands 1999.

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