Geodesic
On a Theorem of Arhangel'skiĭ Concerning Lindelöf P-Spaces
Canadian journal of mathematics, Tome 27 (1975) no. 2, pp. 459-468

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

1. Introduction. In [4] Arhangel'skiĭ proved the remarkable result that every regular space which is hereditarily a Lindelöf p-space has a countable base. As a consequence of the main theorem in this paper, we obtain an analogue of Arhangel'skiĭs result, namely that every regular space which is hereditarily an אi-compact strong ∑-space has a countable net. Under the assumption of the generalized continuum hypothesis (GCH), the main theorem also yields an affirmative answer to Problem 2 in Arhangel'skiĭs paper.In § 3 we introduce and study a new cardinal function called the discreteness character of a space. The definition is based on a property first studied by Aquaro in [1], and for the class of T1 spaces it extends the concept of Kicompactness to higher cardinals. 
Hodel, R. E. On a Theorem of Arhangel'skiĭ Concerning Lindelöf P-Spaces. Canadian journal of mathematics, Tome 27 (1975) no. 2, pp. 459-468. doi: 10.4153/CJM-1975-054-8
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