Geodesic
A Common Extension of Arhangel’skĭ’s Theorem and the Hajnal–Juhász Inequality
Canadian mathematical bulletin, Tome 63 (2020) no. 1, pp. 197-203

Voir la notice de l'article provenant de la source Cambridge University Press

We present a result about $G_{\unicode[STIX]{x1D6FF}}$ covers of a Hausdorff space that implies various known cardinal inequalities, including the following two fundamental results in the theory of cardinal invariants in topology: $|X|\leqslant 2^{L(X)\unicode[STIX]{x1D712}(X)}$ (Arhangel’skiĭ) and $|X|\leqslant 2^{c(X)\unicode[STIX]{x1D712}(X)}$ (Hajnal–Juhász). This solves a question that goes back to Bell, Ginsburg and Woods’s 1978 paper (M. Bell, J.N. Ginsburg and R.G. Woods, Cardinal inequalities for topological spaces involving the weak Lindelöf number, Pacific J. Math. 79(1978), 37–45) and is mentioned in Hodel’s survey on Arhangel’skiĭ’s Theorem (R. Hodel, Arhangel’skii’s solution to Alexandroff’s problem: A survey, Topology Appl. 153(2006), 2199–2217).In contrast to previous attempts, we do not need any separation axiom beyond $T_{2}$.
DOI : 10.4153/S0008439519000420
Mots-clés : cardinality bound, cardinal invariant, cellularity, Lindelöf, weakly Lindelöf, piecewise weakly Lindelöf 
Bella, Angelo; Spadaro, Santi. A Common Extension of Arhangel’skĭ’s Theorem and the Hajnal–Juhász Inequality. Canadian mathematical bulletin, Tome 63 (2020) no. 1, pp. 197-203. doi: 10.4153/S0008439519000420
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