Hereditary separability in Hausdorff continua

D. Daniel; M. Tuncali

doi:10.4995/agt.2012.1638

Hereditary separability in Hausdorff continua

D. Daniel, M. Tuncali

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

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.

Keywords

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

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