caa a22 4500 469069023 CHVBK 20180323132916.0 cr unu---uuuuu 170328e19920201xx s 000 0 eng 10.1007/BF02801567 doi (NATIONALLICENCE)springer-10.1007/BF02801567 Mappings of Baire spaces into function spaces and Kadeč renorming [Elektronische Daten] [I. Namioka, R. Pol] Assuming that there exists in the unit interval [0, 1] a coanalytic set of continuum cardinality without any perfect subset, we show the existence of a scattered compact Hausdorff spaceK with the following properties: (i) For each continuous mapf on a Baire spaceB into (C(K), pointwise), the set of points of continuity of the mapf: B → (C(K), norm) is a denseG δ subset ofB, and (ii)C(K) does not admit a Kadeč norm that is equivalent to the supremum norm. This answers the question of Deville, Godefroy and Haydon under the set theoretic assumption stated above. The Magnes Press, 1992 Namioka I. Department of Mathematics, University of Washington, 98195, Seattle, WA, USA aut Pol R. Wydzial Matematyki U.W., Banacha 2, 00-913, Warszawa 59, Poland aut Israel Journal of Mathematics Springer-Verlag 78/1(1992-02-01), 1-20 0021-2172 78:1<1 1992 78 11856 https://doi.org/10.1007/BF02801567 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF02801567 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Namioka I. Department of Mathematics, University of Washington, 98195, Seattle, WA, USA aut NATIONALLICENCE 700 1- Pol R. Wydzial Matematyki U.W., Banacha 2, 00-913, Warszawa 59, Poland aut NATIONALLICENCE 773 0- Israel Journal of Mathematics Springer-Verlag 78/1(1992-02-01), 1-20 0021-2172 78:1<1 1992 78 11856 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer