Metrizable-like locally convex topologies on C(X)

J. C. Ferrando, S. Gabriyelyan, J. Ka̧kol

Research output: Contribution to journalArticlepeer-review

6 Scopus citations

Abstract

The classic Arens theorem states that the space C(X) of real-valued continuous functions on a Tychonoff space X is metrizable in the compact-open topology τk if and only if X is hemicompact. Less demanding but still applicable problem asks whether τk has an NN-decreasing base at zero (Uα)α∈NN, called in the literature a G-base. We characterize those spaces X for which C(X) admits a locally convex topology T between the pointwise topology τp and the bounded-open topology τb such that (C(X),T) is either metrizable or is an (LM)-space or even has a G-base.

Original languageEnglish
Pages (from-to)105-113
Number of pages9
JournalTopology and its Applications
Volume230
DOIs
StatePublished - 1 Oct 2017

Keywords

  • (LM)-topology
  • Functionally bounded set
  • G-base
  • Hewitt realcompactification
  • K-analytic
  • Metrizable

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