A+ CATEGORY SCIENTIFIC UNIT

Some remarks providing discontinuous maps on some $C_p(X)$ spaces

Volume 79 / 2008

S. Moll Banach Center Publications 79 (2008), 131-133 MSC: 54C05, 54C35. DOI: 10.4064/bc79-0-10

Abstract

Let $X$ be a completely regular Hausdorff topological space and $C_{p}(X)$ the space of continuous real-valued maps on $X$ endowed with the pointwise topology. A simple and natural argument is presented to show how to construct on the space $C_{p}(X)$, if $X$ contains a homeomorphic copy of the closed interval $[0,1]$, real-valued maps which are everywhere discontinuous but continuous on all compact subsets of $C_{p}(X)$.

Authors

  • S. MollDepartamento de Matemática Aplicada
    Universidad Politécnica de Valencia
    E-46022 Valencia, Spain
    e-mail

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