Hereditary separability in Hausdorff continua

D. Daniel

United States

Lamar University

Lamar University, Department of Mathematics, Beaumont, Texas 77710, USA

M. Tuncali

Canada

Nipissing University

Nipissing University, Faculty of Arts and Sciences, North Bay, Ontario P1B 8L7, Canada
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Accepted: 2013-07-29

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Published: 2012-04-15

DOI: https://doi.org/10.4995/agt.2012.1638
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Keywords:

Hereditary separability, Image of compact ordered space, Locally connected continuum, Rim-separability

Supporting agencies:

Tuncali is partially supported by National Science and Engineering Research Council of Canada grants No

141066-2008

Abstract:

We consider those Hausdorff continua S such that each separable subspace of S is hereditarily separable. Due to results of Ostaszewski and Rudin, respectively, all monotonically normal spaces and therefore all continuous Hausdorff images of ordered compacta also have this property. Our study focuses on the structure of such spaces that also possess one of various rim properties, with emphasis given to rim-separability. In so doing we obtain analogues of results of M. Tuncali and I. Loncar, respectively.

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