The Mazurkiewicz Distance and Sets that are Finitely Connected at the Boundary
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) PublishedText
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.
Compactness; Countably connected planar domain; Finitely connected at the boundary; Locally accessible; Locally connected; Mazurkiewicz boundary; Metric space
IdentifiersURN: urn:nbn:se:liu:diva-130310DOI: 10.1007/s12220-015-9575-9ISI: 000378524800007OAI: oai:DiVA.org:liu-130310DiVA: diva2:950491
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 ; NSF [DMS-1200915]2016-07-312016-07-282016-07-31