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Multifunctions and Inverse Cluster Sets

Published online by Cambridge University Press:  20 November 2018

James E. Joseph
James E. Joseph*
Affiliation:
Department of Mathematics Howard University Washington, D.C.20059
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Abstract

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In this paper the notion of inverse cluster set, which was recently introduced and studied for functions by T. R. Hamlett and P. E. Long (Proc. Amer. Math. Soc, 53 (1975), 470-476), is extended to and investigated for multifunctions. We generalize the notion of inverse cluster set, extend to multifunctions and generalize some known results for inverse cluster sets of functions and offer some new results. In the latter sections, compactness generalizations are characterized in terms of inverse cluster sets and some results on connected and conectivity functions are extended to multifunctions.

Keywords

54C6054C1054D1554D2054D25Multifunctionupper-semicontinuousclosed graphinverse cluster set
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 23 , Issue 2 , 01 June 1980 , pp. 161 - 171
Copyright
Copyright © Canadian Mathematical Society 1980

References

1. Gillman, L. and Jerison, M., Rings of continuous functions, Van Nostrand, New York, 1960.Google Scholar
2. Herrington, L. L.,Remarks on H(i) spaces and strongly-closed graphs, Proc. Amer. Math. Soc., 58 (1976), 277-283.Google Scholar
3. Hamlett, T. R.and Long, P. E., Inverse cluster sets, Proc. Amer. Math. Soc, 53 (1975), 470-476.Google Scholar
4. Herrington, L. L. and Long, P. E., Characterizations of H-closed spaces, Proc. Amer. Math. Soc., 48 (1975), 469-475.Google Scholar
5. Joseph, J. E., Multifunctions and cluster sets, Proc. Amer. Math. Soc, 74, (1979) 329-337.Google Scholar
6. Levine, N., A decomposition of continuity in topological spaces, Amer. Math. Monthly 68 (1961), 44-46.Google Scholar
7. Pervin, W. J. and Levine, N., Connected mappings of Hausdorff spaces, Proc. Amer. Math. Soc, 9 (1958), 488-496.Google Scholar
8. Porter, J. and Thomas, J., On H-closed and minimal Hausdroffl spaces, Trans. Amer. Math. Soc, 138 (1969), 159-170.Google Scholar
9. Smithson, R. E., Multifunctions, Nieuw Archief voor Wiskunde(3) 20 (1972), 31-53.Google Scholar
10. Smithson, R. E., Almost and weak continuity for multifunctions, Preprint.Google Scholar
11. Smithson, R. E., Subcontinuity for multifunctions, Pacific J. Math. 61 (1975), 283-288.Google Scholar
12. Smithson, R. E., Connected and connectivity multifunctions, Proc. Amer. Math. Soc, 64 (1977), 146-148 Google Scholar
13. Singal, M. K. and Singal, A. R., Almost continuous mappings, Yokohama Math. J., 16 (1968), 63-73.Google Scholar
14. Veličko, N. V., H-closed topological spaces, Mat. Sb., 70 (112) (1966), 98-112; Amer. Math. Soc. Transi., 78 (Series 2) (1969), 103-118.Google Scholar