Multiplicative linear functionals of continuous functions are countably evaluated

ERCAN Z., ÖNAL S.

TAIWANESE JOURNAL OF MATHEMATICS, vol.12, no.1, pp.173-178, 2008 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 12 Issue: 1
  • Publication Date: 2008
  • Doi Number: 10.11650/twjm/1500602495
  • Journal Name: TAIWANESE JOURNAL OF MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.173-178
  • Middle East Technical University Affiliated: Yes

Abstract

We prove that each nonzero algebra homomorphism pi : C(X) -> R is countably evaluated. This is applied to give a simple and direct proof (from the algebraic view) of the fact that each Lindelof space is realcompact.