On some variations of multifunction continuity
Keywords:Almost â„“âˆ’continuity, K-almost câˆ’continuity, Semi continuity, Super continuity, δâˆ’continuity, Nearly continuity, Change of topology, Multifunction
This paper considers six classes of multifunctions between topological spaces, namely almost â„“âˆ’continuous multifunctions, K-almost câˆ’continuous multifunctions, nearly continuous multifunctions, almost nearly continuous multifunctions, super continuous multifunctions, and δâˆ’continuous multifunctions. We relate these classes of multifunctions to others, and provide characterizations of related concepts especially in terms of appropriate changes of topology.
M. Akdag, On super continuous multifunctions, Acta Math.Hungar. 99(1-2)(2003),143-153.
J. Cao and I.L. Reilly, On δ-continuous multifunctions and paralindel¨ofness, Indian J.Pure Appl. Math. 26, no. 11 (1995), 1099–1110.
D. Carnahan, Locally nearly compact spaces, Boll. Un. Math. Ital. 4 (1972), 146–153.
G. Choquet, Convergences, Ann. Univ. Grenoble 23 (1947-1948), 57–112.
E. Ekici, Nearly continuous multifunctions, Acta Math. Univ. Comenianae LXXII, no. 2 (2003), 229–235.
E. Ekici, Almost nearly continuous multifunctions, Acta Math. Univ. Comeniane LXXIII, no. 2 (2004), 175–186.
D. B. Gauld, c-continuous functions and cocompact topologies, Kyungpook Math. J. 18 (1978), 151–157.
D. B. Gauld, Topologies related to notions of near continuity, Kyungpook Math. J. 21 (1981), 195–204.
D. B. Gauld, M. Mrsevic, I. L. Reilly and M.K. Vamanamurthy, CoLindelöf topologies and â„“âˆ’continuous functions, Glasnik Matematicki 19, no. 39(1984), 297–308.
L. Hola, V. Balaz and T. Neubrunn, Remarks on c-continuous multifunctions, Acta Math. Univ. Comenianae L-LI (1987), 51–58.
A. Kanibir and I. L. Reilly, On almost â„“âˆ’continuous multifunctions, Hacettepe J. Math. Stat. 35, no. 2 (2006), 181–188.
Ch. Konstadilaki-Savvopoulou and I. L. Reilly, Almost â„“âˆ’continuous functions, Glasnik Matematicki 25, no. 45 (1990), 363–370.
Ch. Konstadilaki-Savvopoulou and I. L. Reilly, On almost N-continuous functions, J. Austral. Math. Soc. (SeriesA) 59 (1995), 118–130.
Y. Kucuk, Almost c-continuous multifunctions, Pure and Applied Mathematical Science XXXIX, no.1-2(1994), 1–9.
Y. Kucuk, On some characterizations of δâˆ’continuous multifunctions, Demonstratio Mathematica XXVIII, no. 3 (1995), 587–595.
T. Noiri, Remarks on locally nearly compact spaces, Boll. Un. Mat. Ital. 10, no. 4 (1974), 36–43.
K. Sakalova, Continuity properties of multifunctions, Acta Math. Univ. Comenianae LVI-LVII (1989), 159–165.
N. V. Velicko, H-closed topological spaces, Mat. Sb. 70, no. 112 (1966), 98-112.
How to Cite
This journal is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.