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Relationships among properties of relative paracompactness type. (English) Zbl 1076.54018
As the authors remark, the purpose of this note is to investigate the relationships between various properties of relative paracompactness type introduced by A. V. Arkhangel’skiĭ, and Kh. M. M. Genedi [see also C. Aull, J. Lond. Math. Soc., II. Ser. 1, 155–162 (1969; Zbl 0182.56102), I.Yu. Gordienko, Mosc. Univ. Math. Bull. 46, No. 1, 31–32 (1991); translation from Vestn. Mosk. Univ., Ser. I 1991, No. 1, 42–44 (1991; Zbl 0791.54007)] and the first three authors’ [Topol. Proc. 25, 145–177 (2000; Zbl 1026.54016)]. One of the diagrams presented gives the relations among 17 such properties. Some of the non-implications are established by examples and some others left as open problems.
54D20 Noncompact covering properties (paracompact, Lindelöf, etc.)