Graphs in locally 2connected spaces
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 Carsten Thomassen (Technical University of Denmark)
 Thursday 29 May 2008, 14:3015:30
 MR12.
If you have a question about this talk, please contact Andrew Thomason.
It is wellknown that the property of being locally connected simplifies the structure of a metric space considerably. Nevertheless, a complete description of the locally connected, compact metric spaces seems hopeless. However, a complete description becomes possible if we add the condition that the space does not contain an infinite complete graph and if we also strengthen the local connectivity condition to local 2connectedness, that is, for every element x in the space, and every neighborhood U of x, there exists a neighborhood V of x contained in U such that both V and Vx are connected. Surprisingly, such a space must be locally 2dimensional, that is, it is contained in a 2dimensional surface. Some applications will be given.
This talk is part of the Combinatorics Seminar series.
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