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l.s.c. map; selection; space of probability measures
A negative answer to a question of E.A. Michael is given: A convex $G_\delta$-subset $Y$ of a Hilbert space is constructed together with a l.s.c. map $Y\to Y$ having closed convex values and no continuous selection.
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[2] Michael E.A.: Some problems. in: Open Problems in Topology, J. van Mill, G.M. Reed, eds., North Holland, Amsterdam, 1990, pp.271-278. MR 1078653 | Zbl 1074.11018
[3] Gutev V.G.: Continuous selections, $G_{\delta}$-subsets of Banach spaces and usco mappings. Comment. Math. Univ. Carolinae (1994), 35.3 533-538. MR 1307280
[4] Gutev V.G., Valov V.: Continuous selections and $C$-spaces. Proc. Amer. Math. Soc. (2002), 130 233-242. MR 1855641 | Zbl 0977.54017
[5] Repovš D., Semenov P.V.: Continuous selections of multivalued mappings. in: Recent Progress in General Topology, M. Hušek, J. van Mill, eds., Elsevier Science B.V., 2002, pp.424-461. MR 1970007
[6] von Weizsäcker H.: A note on infinite dimensional convex sets. Math. Scand. (1976), 38 321-324. MR 0428009
[7] Hilton P.J., Wylie S.: Homology Theory. Cambridge University Press, New York, 1960. MR 0115161 | Zbl 0163.17803
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