Rudin, Mary Ellen A biconnected set in the plane. (English) Zbl 0831.54003 Topology Appl. 66, No. 1, 41-48 (1995). Summary: The purpose of this paper is to raise again the question of B. Knaster and C. Kuratowski [Fundam. Math. 2, 206-255 (1921; JFM 48.0209.02)] as to whether there exists a biconnected set in the plane without a dispersion point. Assuming that Martin’s Axiom holds, an example of such a space is constructed which has the additional property of being widely connected. MSC: 54A10 Several topologies on one set (change of topology, comparison of topologies, lattices of topologies) 54E40 Special maps on metric spaces 54C05 Continuous maps Keywords:widely connected space; biconnected set; plane Citations:JFM 48.0209.02 PDFBibTeX XMLCite \textit{M. E. Rudin}, Topology Appl. 66, No. 1, 41--48 (1995; Zbl 0831.54003) Full Text: DOI References: [1] Knaster, B.; Kuratowski, C., Sur les ensembles connexes, Fund. Math., 2, 206-255 (1921) · JFM 48.0209.02 [2] Miller, E. W., Concerning biconnected sets, Fund. Math., 29, 123-133 (1937) · Zbl 0017.13402 [3] Estill, M. E., A biconnected set having no widely connected subset, Bull. Amer. Math. Soc., 59, 346 (1953) [4] Rudin, M. E., A connected subset of the plane, Fund. Math., 46, 15-24 (1958) · Zbl 0227.54029 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.