On planarity of compact, locally connected, metric spaces

Publication: Research - peer-reviewJournal article – Annual report year: 2011

View graph of relations

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.
Original languageEnglish
JournalCombinatorica
Publication date2011
Volume31
Journal number3
Pages365-376
ISSN0209-9683
DOIs
StatePublished
CitationsWeb of Science® Times Cited: 0
Download as:
Download as PDF
Select render style:
APAAuthorCBEHarvardMLAStandardVancouverShortLong
PDF
Download as HTML
Select render style:
APAAuthorCBEHarvardMLAStandardVancouverShortLong
HTML
Download as Word
Select render style:
APAAuthorCBEHarvardMLAStandardVancouverShortLong
Word

ID: 5787817