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The Mazurkiewicz Distance and Sets that are Finitely Connected at the Boundary
Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.ORCID iD: 0000-0002-9677-8321
Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.ORCID iD: 0000-0002-1238-6751
University of Cincinnati, OH 45221 USA.
2016 (English)In: Journal of Geometric Analysis, ISSN 1050-6926, E-ISSN 1559-002X, Vol. 26, no 2, 873-897 p.Article in journal (Refereed) Published
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Abstract [en]

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.

Place, publisher, year, edition, pages
SPRINGER , 2016. Vol. 26, no 2, 873-897 p.
Keyword [en]
Compactness; Countably connected planar domain; Finitely connected at the boundary; Locally accessible; Locally connected; Mazurkiewicz boundary; Metric space
National Category
Mathematical Analysis
Identifiers
URN: urn:nbn:se:liu:diva-130310DOI: 10.1007/s12220-015-9575-9ISI: 000378524800007OAI: oai:DiVA.org:liu-130310DiVA: diva2:950491
Note

Funding Agencies|Swedish Research Council; Swedish Fulbright Commission; Charles Phelps Taft Research Center at the University of Cincinnati; Taft Research Center of the University of Cincinnati; Simons Foundation [200474]; NSF [DMS-1200915]

Available from: 2016-07-31 Created: 2016-07-28 Last updated: 2016-07-31

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