On the Menger and almost Menger properties in locales

• Bayih, Tilahun ^[1] ; Dube, Themba ^[1] ; Ighedo, Oghenetega ^[1]
  1. [1] University of South Africa
• Localización: Applied general topology, ISSN-e 1989-4147, ISSN 1576-9402, Vol. 22, Nº. 1, 2021, págs. 199-221
• Idioma: inglés
• Enlaces
  • Texto completo
• Resumen

  • The Menger and the almost Menger properties are extended to locales. Regarding the former, the extension is conservative (meaning that a space is Menger if and only if it is Menger as a locale), and the latter is conservative for sober TD-spaces. Non-spatial Menger (and hence almost Menger) locales do exist, so that the extensions genuinely transcend the topological notions. We also consider projectively Menger locales, and show that, as in spaces, a locale is Menger precisely when it is Lindelöf and projectively Menger. Transference of these properties along localic maps (via direct image or pullback) is considered.