caa a22 4500 445358572 CHVBK 20180317142908.0 cr unu---uuuuu 170323e20110501xx s 000 0 eng 10.1007/s00493-011-2563-1 doi (NATIONALLICENCE)springer-10.1007/s00493-011-2563-1 On planarity of compact, locally connected, metric spaces [Elektronische Daten] [R. Richter, Brendan Rooney, Carsten Thomassen] Independently, Claytor [Ann. Math. 35 (1934), 809-835] and Thomassen [Combinatorica 24 (2004), 699-718] proved that a 2-connected, compact, locally connected metric space is homeomorphic to a subset of the sphere if and only if it does not contain K 5 or K 3;3. The "thumbtack space” consisting of a disc plus an arc attaching just at the centre of the disc shows the assumption of 2-connectedness cannot be dropped. In this work, we introduce "generalized thumbtacks” and show that a compact, locally connected metric space is homeomorphic to a subset of the sphere if and only if it does not contain K 5, K 3;3, or any generalized thumbtack, or the disjoint union of a sphere and a point. János Bolyai Mathematical Society and Springer Verlag, 2011 Richter R. Faculty of Mathematics, University of Waterloo, N2L 3G1, Waterloo, ON, USA aut Rooney Brendan Faculty of Mathematics, University of Waterloo, N2L 3G1, Waterloo, ON, USA aut Thomassen Carsten Department of Mathematics, Technical University of Denmark, 2800, Kgs. Lyngby, Denmark aut Combinatorica Springer-Verlag 31/3(2011-05-01), 365-376 0209-9683 31:3<365 2011 31 493 https://doi.org/10.1007/s00493-011-2563-1 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00493-011-2563-1 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Richter R. Faculty of Mathematics, University of Waterloo, N2L 3G1, Waterloo, ON, USA aut NATIONALLICENCE 700 1- Rooney Brendan Faculty of Mathematics, University of Waterloo, N2L 3G1, Waterloo, ON, USA aut NATIONALLICENCE 700 1- Thomassen Carsten Department of Mathematics, Technical University of Denmark, 2800, Kgs. Lyngby, Denmark aut NATIONALLICENCE 773 0- Combinatorica Springer-Verlag 31/3(2011-05-01), 365-376 0209-9683 31:3<365 2011 31 493 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer