The Locally Connected Compact Metric Spaces Embeddable In The Plane

We prove that a 2-connected, locally connected, compact topological space M is homeomorphic to a subset of the 2-sphere if and only if M is metrizable and contains none of the Kuratowski graphs K 5 and K 3,3.

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Correspondence to Carsten Thomassen.

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Thomassen, C. The Locally Connected Compact Metric Spaces Embeddable In The Plane. Combinatorica 24, 699–718 (2004). https://doi.org/10.1007/s00493-004-0042-7

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Mathematics Subject Classification (2000):

  • 05C10
  • 57M15