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.
Citation: Hanfeng Wang, Jing Zhang. The source number of a Tychonoff space in its compactifications[J]. Electronic Research Archive, 2026, 34(1): 424-432. doi: 10.3934/era.2026020
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.
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Hanfeng Wang, Jing Zhang. The source number of a Tychonoff space in its compactifications[J]. Electronic Research Archive, 2026, 34(1): 424-432. doi: 10.3934/era.2026020
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