Geodesic
Paracompactness in Locally Lindelöf Spaces
Canadian journal of mathematics, Tome 38 (1986) no. 3, pp. 719-727

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

This paper contains a set of results concerning paracompactness of locally nice spaces which can be proved by (variations on) the technique of “stationary sets and chaining” combined with other techniques available at the present stage of knowledge in the field. The material covered by the paper is arranged in three sections, each containing, in essence, one main result.The main result of Section 1 says that a locally Lindelöf, submeta-Lindelöf ( = δθ-refinable) space is paracompact if and only if it is strongly collectionwise Hausdorff. Two consequences of this theorem, respectively, answer a question raised by Tall [7], and strengthen a result of Watson [9]. In the last two sections, connected spaces are dealt with. The main result of the second section can be best understood from one of its consequences which says that under 2ωl > 2ω , connected, locally Lindelöf, normal Moore spaces are metrizable. 
Balogh, Zoltán. Paracompactness in Locally Lindelöf Spaces. Canadian journal of mathematics, Tome 38 (1986) no. 3, pp. 719-727. doi: 10.4153/CJM-1986-037-7
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