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Journal of Convex Analysis 26 (2019), No. 4, 1347--1348 Copyright Heldermann Verlag 2019 Examples of Nondistinguished Function Spaces Cp(X) Juan Carlos Ferrando Centro de Investigación Operativa, Universidad Miguel Hernández, 03202 Elche, Spain jc.ferrando@umh.es Jerzy Kakol Faculty of Mathematics and Informatics, A. Mickiewicz University, 61-614 Poznan, Poland and: Institute of Mathematics, Czech Academy of Sciences, Prague, Czech Republic kakol@amu.edu.pl Stephen A. Saxon Dept. of Mathematics, University of Florida, Gainesville, FL 32611, U.S.A. stephen_saxon@yahoo.com [Abstract-pdf] In the pointwise topology, familiar function spaces $C_{p}(\beta\mathbb{N})$, $C_{p}(\mathbb{R})$, $C_{p}\left[ 0,1\right] $, and $C_{p}(\text{Cantor set})$ are not distinguished. Keywords: Distinguished locally convex space, pointwise topology, strongest locally convex topology, function spaces. MSC: 46A08, 46E10; 54C35 [ Fulltext-pdf (66 KB)] for subscribers only. |