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The source number of a Tychonoff space in its compactifications
Electronic Research Archive 2026, 34(1): 424-432
Published: 14 January 2026
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The source number s o ( X ) of a Tychonoff space X denotes the minimal cardinal τ such that X has an open source S in some compactification b X for which | S | τ. In this paper some properties of source numbers are studied. Among other things, we showed that the equalities w ( X ) = n w ( X ) s o ( X ) and w ( X ) = s o ( X ) N a g ( X ) i w ( X ) hold for every Tychonoff space X, where w ( X ), n w ( X ), i w ( X ), N a g ( 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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