Journal article
Classification of locally 2-connected compact metric spaces
In
Combinatorica
—
2005, Volume 25, Issue 1, pp. 85-103
Abstract
The aim of this paper is to prove that, for compact metric spaces which do not contain infinite complete graphs, the (strong) property of being "locally 2-dimensional" is guaranteed just by a (weak) local connectivity condition. Specifically, we prove that a locally 2-connected, compact metric space M either contains an infinite complete graph or is surface like in the following sense: There exists a unique surface S such that S and M. contain the same finite graphs.
Moreover, M is embeddable in S, that is, M is homeomorphic to a subset of S.
| Language: | English |
|---|---|
| Publisher: | Springer-Verlag |
| Year: | 2005 |
| Pages: | 85-103 |
| Journal subtitle: | An International Journal on Combinatorics and the Theory of Computing |
| ISSN: | 14396912 and 02099683 |
| Types: | Journal article |
| DOI: | 10.1007/s00493-005-0007-5 |
| ORCIDs: | Thomassen, Carsten |
