Hereditary separability in Hausdorff continua

Hereditary separability in Hausdorff continua

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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 read more monotonically normal spaces and therefore all continuous Hausdorff images of ordered compacta also have this property.Our study focuses on the structure of such here 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.