Journal article
On planarity of compact, locally connected, metric spaces
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.
Language: | English |
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Publisher: | Springer-Verlag |
Year: | 2011 |
Pages: | 365-376 |
ISSN: | 14396912 and 02099683 |
Types: | Journal article |
DOI: | 10.1007/s00493-011-2563-1 |
ORCIDs: | Thomassen, Carsten |