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SUMMARY:Graphs in locally 2-connected spaces - Carsten Thomassen (Technica
 l University of Denmark)
DTSTART:20080529T133000Z
DTEND:20080529T143000Z
UID:TALK11972@talks.cam.ac.uk
CONTACT:Andrew Thomason
DESCRIPTION:It is well-known 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 seem
 s hopeless. However\, a complete description becomes possible if we add th
 e condition that the space does not contain an infinite complete graph and
  if we also strengthen the local connectivity condition to local 2-connect
 edness\, that is\, for every element x in the space\, and every neighborho
 od U of x\, there exists a neighborhood V of x contained in U such that bo
 th V and V-x are connected. Surprisingly\, such a space must be locally 2-
 dimensional\, that is\, it is contained in a 2-dimensional surface. Some a
 pplications will be given.\n
LOCATION:MR12
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