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arXiv · 1311.5122

The Mazurkiewicz distance and sets that are finitely connected at the boundary

Anders Björn·Jana Björn·Nageswari Shanmugalingam
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Abstract

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.

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Anders Björn, Jana Björn, Nageswari Shanmugalingam. 2013-11-20. The Mazurkiewicz distance and sets that are finitely connected at the boundary. https://doi.org/10.1007/s12220-015-9575-9

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