The Mazurkiewicz distance and sets that are finitely connected at the boundary. (English) Zbl 1342.30054
Summary: We study local connectedness, local accessibility and finite connectedness at the boundary, in relation to the compactness of the Mazurkiewicz completion of a bounded domain in a metric space. For countably connected planar domains we obtain a complete characterization. It is also shown exactly which parts of this characterization fail in higher dimensions and in metric spaces.
MSC:
| 30L99 | Analysis on metric spaces |
References:
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