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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

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

Stephen A. Saxon
Dept. of Mathematics, University of Florida, Gainesville, FL 32611, U.S.A.


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

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