A homogeneous space that is one-dimensional but not cohesive

• Autores: Jan J. Dijkstra
• Localización: Houston journal of mathematics, ISSN 0362-1588, Vol. 32, Nº 4, 2006, págs. 1093-1099
• Idioma: inglés
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• Resumen

  • A separable metric space is called cohesive if every point of the space has a neighbourhood that fails to contain nonempty clopen subsets of the space. A topological group is cohesive if and only if it is not zero-dimensional. We present a homogeneous, one-dimensional, almost zero-dimensional space that is not cohesive.

    We also show that a complete homogeneous space is cohesive if and only if it is not zero-dimensional.