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A topological space is strongly paracompact if and only if for any monotone increasing open cover of it there exists a star-finite open refinement. (English) Zbl 1174.54013
Summary: We get the following result. A topological space is strongly paracompact if and only if for any monotone increasing open cover of it there exists a star-finite open refinement.
MSC:
54D20Noncompact covering properties (paracompact, Lindelöf, etc.)
References:
[1]Ryszard Engelkin: General Topology. Panstwowe Wydawnictwo Naukowe, 1977.
[2]Yoshikazu Yasui: Generalization Paracompactness. Chapter 13 of Topics in General topology (Editor by Kitti Morit and Jun-iti Nagata), Elsever Science Publishers B.V., 1989.
[3]Wang Shu-tang, Dai Jin-sheng and Wang Shang-zhi: Principles of General Topology. Science and Technique Press of Shannxi, China, 1985.
[4]Jiang Ji-guang: Especial Topics of General Topology. Education Press of Sichuan, China, 1991.