Rudin, Mary Ellen Two nonmetrizable manifolds. (English) Zbl 0708.54012 Topology Appl. 35, No. 2-3, 137-152 (1990). The author showed in 1979 that the existence of separable perfectly normal non-metrizable manifolds is undecidable in ZFC [Houston J. Math. 5, 249-252 (1979; Zbl 0418.03036)]. Here it is shown that a separable normal nonmetrizable manifold exists in ZFC. The other nonmetrizable manifold has been constructed using \(\diamondsuit^+\). It is normal but not collectionwise normal. As was shown by F. D. Tall [Handbook of set-theoretic topology, 685-732 (1984; Zbl 0552.54011)], adding weakly compact many random reals, normal implies collectionwise normal in manifolds. Reviewer: A.Szymański Cited in 1 Document MSC: 54D15 Higher separation axioms (completely regular, normal, perfectly or collectionwise normal, etc.) 54A35 Consistency and independence results in general topology 03E45 Inner models, including constructibility, ordinal definability, and core models Keywords:separable normal nonmetrizable manifold; collectionwise normal manifold; ZFC Citations:Zbl 0418.03036; Zbl 0552.54011 PDFBibTeX XMLCite \textit{M. E. Rudin}, Topology Appl. 35, No. 2--3, 137--152 (1990; Zbl 0708.54012) Full Text: DOI References: [1] Balogh, Z., Locally nice spaces under Martin’s Axiom, Comment. Math. Univ. Carolin., 24, 1, 63-87 (1983) · Zbl 0529.54006 [3] van Douwen, E.; Wicke, H., A real weird topology on the reals, Houston J. Math., 3, 141-151 (1977) · Zbl 0345.54036 [4] Juhász, I.; Kunen, K.; Rudin, M. E., Two more hereditarily separable non-Lindelöf spaces, Canad. J. Math., 18, 5, 998-1005 (1976) · Zbl 0336.54040 [5] Rudin, M. E., The undecidability of the existence of a perfectly normal nonmetrizable manifold, Houston J. Math., 5, 2, 249-252 (1979) · Zbl 0418.03036 [6] Rudin, M. E., Two problems of Dowker, Proc. Amer. Math. Soc., 91, 1, 155-158 (1984) · Zbl 0554.54006 [7] Rudin, M. E., A nonmetrizable manifold from ◊\(^+\), Topology Appl., 28, 105-112 (1988) · Zbl 0637.54004 [8] Rudin, M. E.; Zenor, P., A perfectly normal nonmetrizable manifold, Houston J. Math., 2, 1, 129-134 (1976) · Zbl 0315.54028 [9] Tall, F., Normality versus collectionwise normality, (Kunen, K.; Vaughan, J., Handbook of Set-Theoretic Topology, 702 (1984), North-Holland: North-Holland Amsterdam), Theorem 3.2. · Zbl 0552.54011 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.