Balogh, Zoltan T. A small Dowker space in ZFC. (English) Zbl 0876.54016 Proc. Am. Math. Soc. 124, No. 8, 2555-2560 (1996). A hereditarily normal, \(\sigma\)-discrete Dowker space is constructed. It is small in the sense that it has cardinality of the continuum \(c\). A normal Hausdorff space is said to be a Dowker space if its product with the unit interval is not normal (equivalently, if it is not countably paracompact). In 1951, C. H. Dowker raised a problem whether there is a Dowker space or not. It was Mary Ellen Rudin who first proved the existence of such a space in 1971. Her space has cardinality and weight \(\aleph_{\omega}^{\omega}\). She asked whether there exist Dowker spaces with small cardinal functions (cardinality, weight, character, etc) or not. After then there have been plenty of activities in search of small Dowker spaces. Many small Dowker spaces have been constructed in various models of set theory. But her example has been only a ZFC Dowker space. In this paper, the author makes great progress by giving a new ZFC Dowker space mentioned above. His construction is quite different from Rudin’s one. He uses an excellent combinatorial technique, in which the idea of elementary submodels plays an important role. Recently M. Kojman and S. Shelah showed the existence of a Dowker space of cardinality and weight \(\aleph_{\omega + 1}\), which is a subspace of Rudin’s example. It is still open whether there is a Dowker space of cardinality \(\aleph_1\) in ZFC or not. Reviewer: K.Tamano (Yokohama) Cited in 4 ReviewsCited in 9 Documents MSC: 54D15 Higher separation axioms (completely regular, normal, perfectly or collectionwise normal, etc.) 54D20 Noncompact covering properties (paracompact, Lindelöf, etc.) Keywords:countably paracompact; small Dowker space; hereditarily normal; elementary submodel PDFBibTeX XMLCite \textit{Z. T. Balogh}, Proc. Am. Math. 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