Abstract
We prove that for a compact Hausdorff space X, if λc(X)<w(X) for every infinite cardinal λ<w(X) and λc(X)<cf(w(X)) for every infinite cardinal λ<cf(w(X)), then Tikhonov cube [0,1]w(X) is a continuous image of X, in particular the cardinality of X is just 2w(X). As an application of this result, we consider elementary submodel spaces and improve Tall's result in [17].
| Original language | English |
|---|---|
| Pages (from-to) | 41-55 |
| Number of pages | 15 |
| Journal | Topology and its Applications |
| Volume | 174 |
| DOIs | |
| Publication status | Published - 2014 Sept 1 |
| Externally published | Yes |
Keywords
- Compact space
- Countable chain condition
- Dyadic system
- Elementary submodel space
- Independent family
- Precaliber
ASJC Scopus subject areas
- Geometry and Topology