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Keywords:
uniform space; multifunctions; decomposition theorem; quasicontinuity; multivalued map
Summary:
The main results presented in this paper concern multivalued maps. We consider the cliquishness, quasicontinuity, almost continuity and almost quasicontinuity; these properties of multivalued maps are characterized by the analogous properties of some real functions. The connections obtained are used to prove decomposition theorems for upper and lower quasicontinuity.
References:
[1] D. Andrijević: Semi-preopen sets. Mat. Vestnik 38 (1986), 24-32.
[2] J. Borsík J. Doboš: On decomposition of quasicontinuity. Real Anal. Exch. 16 (1990-91), 292-305. MR 1087494
[3] J. Ewert: On quasi-continuous and cliquish maps with values in uniform spaces. Bull. Polish Acad. Sci. Math. 32 (1984), 81-88. MR 0766984 | Zbl 0579.54008
[4] J. Ewert: Quasi-continuity of multivalued maps with respect to the qualitative topology. Acta Math. Hungarica 56 (1990), 39-44. DOI 10.1007/BF01903703 | MR 1100774 | Zbl 0724.54016
[5] J. Ewert: On almost quasicontinuity of functions. Tatra Mountains Math. Publ. 2 (1993), 81-91. MR 1251042 | Zbl 0835.54010
[6] L. A. Fudali: On cliquish functions on product spaces. Math. Slovaca 33 (1983), 53-58. MR 0689278 | Zbl 0512.54007
[7] H. Hashimoto: On the *-topology and its application. Fundam. Math. 91 (1976), 5-10. MR 0413058
[8] T. Husain: Almost continuous mappings. Prace Mat. 10 (1966), 1-7. MR 0220256 | Zbl 0138.17601
[9] S. Kempisty: Sur les fonctions quasi-continues. Fundam. Math. 19 (1932), 184-197.
[10] N. Levine: Semi-open sets and semi-continuity in topological spaces. Amer. Math. Monthly 70 (1963), 36-41. DOI 10.2307/2312781 | MR 0166752 | Zbl 0113.16304
[11] J. S. Lipiński T. Šalát: On the points of quasi-continuity and cliquishness of functions. Czechoslov. Math. J. 21 (1971), 484-489. MR 0287517
[12] T. Neubrunn: Quasicontinuity. Real Anal. Exch. 14 (1988-89), 259-306. MR 0995972
[13] A. Neubrunnová: On quasicontinuous and cliquish functions. Časopis Pěst. Mat. 99 (1974), 109-114. MR 0360948
[14] A. Neubrunnová T. Šalát: On almost quasicontinuity. Math. Bohemica 117 (1992), 197-205. MR 1165897
[15] J. C. Oxtoby: Measure and category. New York-Heidelberg-Berlin, 1971. Zbl 0217.09201
[16] V. Popa: H-almost continuous multifunctions. Stud. Cerc. Mat. 32 (1980), 103-109. MR 0581500 | Zbl 0435.54014
[17] J. Smítal E. Stanová: On almost continuous functions. Acta Math. Univ. Comenianae 37 (1980), 147-156. MR 0645781
[18] H. P. Thielman: Types of functions. Amer. Math. Monthly 60 (1953), 156-161. DOI 10.2307/2307568 | MR 0052495 | Zbl 0051.13801
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