Covering by discrete and closed discrete sets
- Autori: SPADARO, SANTI DOMENICO
- Anno di pubblicazione: 2009
- Tipologia: Articolo in rivista
- OA Link: http://hdl.handle.net/10447/480954
Abstract
Say that a cardinal number k is emph{small} relative to the space X if k is smaller than the least cardinality of a non-empty open set in X. We prove that no Baire metric space can be covered by a small number of discrete sets, and give some generalizations. We show a ZFC example of a regular Baire σ-space and a consistent example of a normal Baire Moore space which can be covered by a small number of discrete sets. We finish with some remarks on linearly ordered spaces.