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Upper and lower almost cl-supercontinuous multifunctions

Wybrane pełne teksty z tego czasopisma
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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The notion of almost cl-supercontinuity (≡ almost clopen continuity) of functions (Acta Math. Hungar. 107 (2005), 193–206; Applied Gen. Topology 10 (1) (2009), 1–12) is extended to the realm of multifunctions. Basic properties of upper (lower) almost 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) almost cl-supercontinuity of multifunctions from that of other strong variants of continuity of multifunctions which already exist in the literature.
Wydawca
Rocznik
Strony
407--421
Opis fizyczny
Bibliogr. 30 poz., rys.
Twórcy
autor
  • Department of Mathematics, Hindu College, University of Delhi, Delhi 110007, India
autor
  • Department of Mathematics, University of Delhi, Delhi 110007, India
Bibliografia
  • [1] N. Ajmal, J. K. Kohli, Properties of hyperconnected spaces, their mappings into Haus-dorff spaces and embeddings into hyperconnected spaces, Acta Math. Hungar. 60 (1-2) (1992), 41–49.
  • [2] M. Akdağ, On supercontinuous multifunctions, Acta Math. Hungar. 99 (1-2) (2003), 143–153.
  • [3] M. Akdağ, On upper and lower z-supercontinuous multifunctions, Kyungpook Math. J. 45 (2005), 221–230.
  • [4] M. Akdağ, On upper and lower Dδ-supercontinuous multifunctions, Miskolc Mathematical Notes 7 (2006), 3–11.
  • [5] M. Akdağ, Weak and strong forms of continuity of multifunctions, Chaos Solitons Fractals 32 (2007), 1337–1344.
  • [6] V. Balaz, L’. Hola, T. Neubrunn, Remarks on c-upper semicontinuous multifunctions, Acta Math. Univ. Comenian. (N.S.) 50/51 (1987), 159–165.
  • [7] D. Carnahan, Locally nearly compact spaces, Boll. Un. Mat. Ital. 6 (1972), 146–153.
  • [8] E. Ekici, Generalizations of perfectly continuous, regular set connected and clopen functions, Acta Math. Hungar. 107 (2005), 193–206.
  • [9] S. Fomin, Extensions of topological spaces, Ann. of Math. 44 (1943), 471–480.
  • [10] L. Gillman, M. Jerison, Rings of Continuous Function, D. Van Nostrand Company, New York, 1960.
  • [11] L. Górniewicz, Topological Fixed Point Theory of Multivalued Mappings, Kluwer Academic Publishers, Dordrect, The Netherlands, 1999.
  • [12] L’. Hola, Some conditions that imply continuity of almost continuous multifunctions, Acta Mat. Univ. Comenian. 52/53 (1987), 159–165.
  • [13] L’. Hola, Remarks on almost continuous multifunctions, Math. Slovaca 38 (1988), 325–331.
  • [14] J. K. Kohli, Localization, generalizations and factorizations of zero dimensionality, preprint.
  • [15] J. K. Kohli, C. P. Arya, Upper (lower) cl-supercontinuous multifunctions, Appl. Gen. Topol., to appear.
  • [16] J. K. Kohli, D. Singh, C. P. Arya, Upper (lower) quasi cl-supercontinuous multifunctions, Appl. Gen. Topol., to appear.
  • [17] J. K. Kohli, C. P. Arya, Strongly continuous and upper (lower) perfectly continuous multifunctions, Studii Si Cercetari Ser. Mat. 19 (2009).
  • [18] J. K. Kohli, C. P. Arya, Generalizations of z-supercontinuous and Dδ-supercontinuous multifunctions, preprint.
  • [19] J. K. Kohli, C. P. Arya, Upper and lower (almost) completely continuous multifunctions, in preparation.
  • [20] J. K. Kohli, D. Singh, Almost cl-supercontinuous functions, Appl. Gen. Topol. 10 (1) (2009), 1–12.
  • [21] J. K. Kohli, D. Singh, δ-perfectly continuous functions, Demonstratio Math. 42 (2009), 221–231.
  • [22] J. K. Kohli, D. Singh, R. Kumar, Generalization of z-supercontinuous functions and Dδ-supercontinuous functions, Appl. Gen. Topol. 9 (2) (2008), 239–251.
  • [23] Y. Kucuk, On strongly θ-continuous multifunctions, Pure Appl. Math. Sci. 40 (1994), 43–54.
  • [24] Y. Kucuk, On some characterizations of δ-continuous multifunctions, Demonstratio Math. 28 (1995), 587–595.
  • [25] M. K. Singal, A. Mathur, On nearly compact spaces, Boll. Unione Mat. Ital. 2 (4) (1969), 702–710.
  • [26] M. K. Singal, A. R. Singal, Almost continuous mappings, Yokohama Math. J. 16 (1968), 63–73.
  • [27] D. Singh, cl-supercontinuous functions, Appl. Gen. Topol. 8 (2) (2007), 293–300.
  • [28] D. Singh, Almost perfectly continuous functions, Quaestiones Math. 33 (2010), 211–221.
  • [29] R. Staum, The algebra of bounded continuous functions into non Archimedean field, Pacific J. Math. 50 (1) (1974), 169–185.
  • [30] L. A. Steen, J. A. Seebach Jr., Counter Examples in Topology, Springer, New York, 1978.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-bf98aed8-4d1e-4dee-94e7-b67fc8e03b47
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