Balogh, Z.; Rudin, M. E. Monotone normality. (English) Zbl 0769.54022 Topology Appl. 47, No. 2, 115-127 (1992). The bulk of this paper is devoted to a proof of the following remarkable theorem: Every open cover \(\mathcal U\) of a monotonically normal space \(X\) has a \(\sigma\)-disjoint open partial refinement \(\mathcal V\) such that \(X\backslash\bigcup{\mathcal V}\) is the union of a discrete family of stationary subsets of regular uncountable cardinals.This result has many consequences; we mention two: 1) Every monotonically normal space has the shrinking property and 2) a monotonically normal space is paracompact iff it does not contain a closed subspace homeomorphic to a stationary subset of a regular uncountable cardinal. Several new characterizations of paracompactness for monotonically normal spaces drop out. Reviewer: K.P.Hart (Delft) Cited in 1 ReviewCited in 61 Documents MSC: 54D15 Higher separation axioms (completely regular, normal, perfectly or collectionwise normal, etc.) 54D20 Noncompact covering properties (paracompact, Lindelöf, etc.) 54B10 Product spaces in general topology 54A25 Cardinality properties (cardinal functions and inequalities, discrete subsets) 54D45 Local compactness, \(\sigma\)-compactness Keywords:monotone normality; shrinking property; paracompactness PDFBibTeX XMLCite \textit{Z. Balogh} and \textit{M. E. Rudin}, Topology Appl. 47, No. 2, 115--127 (1992; Zbl 0769.54022) Full Text: DOI References: [1] Fleissner, F., The normal Moore space conjecture and large cardinals, (Kunen, K.; Vaughan, J. E., Handbook of Set-Theoretic Topology (1984), North-Holland: North-Holland Amsterdam), 750-760 · Zbl 0562.54039 [2] Hart, K. P., Strong collectionwise normality and M.E. Rubin’s Dowker space, Proc. Amer. Math. Soc., 83, 802-806 (1981) · Zbl 0468.54011 [3] Kemoto, N., On \(B\)-property, Questions Answers Gen. Topology, 7, 71-78 (1989) · Zbl 0760.54017 [4] Lutzer, D., Ordered topological spaces, (Surveys in General Topology (1980), Academic Press: Academic Press New York), 247-295 · Zbl 0472.54020 [5] Nagami, K., Paracompactness and strong screenability, Nagoya Math. J., 8, 83-88 (1955) · Zbl 0064.41102 [6] Navy, C., Paracompactness in para-Lindelöf spaces, (Thesis (1981), University of Wisconsin: University of Wisconsin Madison, WI) [7] Palenz, D., Monotone normality and paracompactness, Topology Appl., 14, 171-182 (1982) · Zbl 0491.54013 [8] Rudin, M. E., Dowker spaces, (Kunen, K.; Vaughan, J. E., Handbook of Set-Theoretic Topology (1984), North-Holland: North-Holland Amsterdam), 761-780 · Zbl 0566.54009 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.