The source number of a Tychonoff space in its compactifications
Abstract
The source number $ so(X) $ of a Tychonoff space $ X $ denotes the minimal cardinal $ \tau $ such that $ X $ has an open source $ \mathcal{S} $ in some compactification $ bX $ for which $ |\mathcal{S}|\leq\tau $. In this paper some properties of source numbers are studied. Among other things, we showed that the equalities $ w(X) = nw(X) so(X) $ and $ w(X) = so(X) Nag(X) iw(X) $ hold for every Tychonoff space $ X $, where $ w(X) $, $ nw(X) $, $ iw(X) $, $ Nag(X) $ denote the weight, network weight, $ i $-weight, and Nagami number of a space $ X $, respectively. Some corollaries about the two statements were obtained.
Fields of Study & Subjects
Advanced Topology and Set Theory
Advanced Banach Space Theory
Advanced Harmonic Analysis Research
Publication details
- Journal / source
- Electronic Research Archive
- Volume
- 34
- Issue
- 1
- Pages
- 424–432
- Publication date
- 1 January 2026