Minimal basically disconnected covers of countably locally weakly Lindelof spaces

  • Published : 2003.03.01

Abstract

Observing that if f: $Y{\leftrightarro}$Χ is a covering map and Χ is a countably locally weakly Lindelof space, then Y is countably locally weakly Lindelof and that every dense countably weakly Lindelof subspace of a basically disconnected space is basically disconnected, we show that for a countably weakly Lindelof space Χ, its minimal basically disconnected cover ${\bigwedge}$Χ is given by the filter space of fixed ${\sigma}Ζ(Χ)^#$- ultrafilters.

Keywords

References

  1. Pasific J. Math. v.28 F'-space and their products with P=space W. W. Comport;N. Hindman;S. Negrepontis
  2. Topol. and its Appl. v.72 Minimal covers and filter spaces C. I. Kim
  3. Extensions and Absolutes of Hausdorff J. Porter;R. G. Woods
  4. Topol. and its Appl. v.17 The smallest basically disconnected preimage of a space J. Vermeer