×

A nonmetrizable manifold \(\diamond ^ +\). (English) Zbl 0637.54004

Assuming \(\diamond^+\), a perfectly normal 3-dimensional manifold M is constructed with the property that \(M=\cup_{\alpha <\omega_ 1}M_{\alpha}\) where each \(M_{\alpha}\) is an open connected metric subspace of M with \(\overline{\cup_{\beta <\alpha}M_{\beta}}\subsetneqq M_{\alpha}\).

MSC:

54A35 Consistency and independence results in general topology
57N10 Topology of general \(3\)-manifolds (MSC2010)
54D15 Higher separation axioms (completely regular, normal, perfectly or collectionwise normal, etc.)
03E45 Inner models, including constructibility, ordinal definability, and core models
PDFBibTeX XMLCite
Full Text: DOI

References:

[2] Rudin, M. E.; Zenor, P., A perfectly normal nonmetrizable manifold, Houston J. Math., 2, 203-210 (1976) · Zbl 0315.54028
[3] Rudin, M. E., The undecidability of the existence of a perfectly normal nonmetrizable manifold, Houston J. Math., 5, 249-252 (1979) · Zbl 0418.03036
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.