Czarnowska, Joanna Intermediate value property and functional connectedness of multivalued maps. (English) Zbl 0889.54013 Math. Slovaca 46, No. 2-3, 269-277 (1996). Unions, intersections, limits, algebraic sums and products of multivalued maps which either both are functionally connected, or have the intermediate value property are considered. It is shown that the composition of a continuous and a functionally connected function need not be functionally connected. Conditions equivalent to the intermediate value property of multivalued maps and some conditions under which upper continuity and the intermediate value property of multivalued maps are equivalent, are given. MSC: 54C60 Set-valued maps in general topology Keywords:functional connectedness points; Darboux property × Cite Format Result Cite Review PDF Full Text: EuDML References: [1] BRUCKNER A. M.: Differentiation of Real Functions. Lecture Notes in Math. 659, Springer, New York-Berlin, 1987, p. 9. · Zbl 0382.26002 [2] CZARNOWSKA J.: Functional connectedness and Darboux property of multivalued functions. Period. Math. Hung. 26 (1993), 101-110. · Zbl 0847.54018 · doi:10.1007/BF01876311 [3] CZARNOWSKA J.-KWIECIŃSKA G.: On the Darboux property of multivalued functions. Demonstratio Math. XXV (1992), 193-199. · Zbl 0765.54010 [4] EWERT J.-LIPIŃSKI J.: On the continuity of Darboux multifunctions. Real Anal. Exchange 13 (1987/88), 122-125. [5] JASTRZȨBSKI J. M.-JEDRZEJEWSKI J. M.: Functionally connected functions. Zeszyty Nauk. Politech. Śląskiej. Mat. Fiz. 48 (1986), 73-79. · Zbl 0777.26008 [6] KURATOWSKI K.: Some remarks on the relation of classical set-valued mappings to the Baire classification. Colloq. Math. 42 (1979), 273-277. · Zbl 0445.28010 [7] LIPIŃSKI J. S.: Une remarque sur la continuite et connexite. Colloq. Math. 19 (1968), 251-253. · Zbl 0179.51402 [8] PU H. W.-PU H. H.: On Darboux continuity and continuity. J. Math. Anal. Appl. 84 (1981), 59-62. · Zbl 0494.54010 · doi:10.1016/0022-247X(81)90151-7 [9] ZAHORSKI Z.: Sur la premiere derivee. Trans. Amer. Math. Soc. 69 (1950), 1-54. · Zbl 0038.20602 · doi:10.2307/1990595 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.