The source number of a Tychonoff space in its compactifications

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Abstract

The source number so(X) of a Tychonoff space X denotes the minimal cardinal τ such that X has an open source S in some compactification bX for which |$\mathcal{S}$| ≤ τ. 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.

Keywords

source number / Nagami number / weight / network weight / compactification

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