On the definability of Menger spaces which are not sigma-compact

Tall F. D., TOKGÖZ S.

TOPOLOGY AND ITS APPLICATIONS, vol.220, pp.111-117, 2017 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 220
  • Publication Date: 2017
  • Doi Number: 10.1016/j.topol.2017.02.018
  • Journal Name: TOPOLOGY AND ITS APPLICATIONS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.111-117
  • Keywords: Menger, sigma-compact, Projective set of reals, Analytic, Co-analytic, K-analytic, Determinacy, p-Space, s-Space, Sigma-space, LINDELOF SPACES, P-SPACES, HUREWICZ, REMAINDERS
  • Hacettepe University Affiliated: Yes

Abstract

Hurewicz proved completely metrizable Menger spaces are a-compact. We extend this to Oech-complete Menger spaces, and consistently, to projective metrizable Menger spaces. On the other hand, it is consistent that there is a co-analytic Menger metrizable space that is not a-compact. (C) 2017 Elsevier B.V. All rights reserved.