On Metrizability of Images of Ordered Compacta

• Autores: Dale Daniel
• Localización: Houston journal of mathematics, ISSN 0362-1588, Vol. 32, Nº 4, 2006, págs. 1047-1059
• Idioma: inglés
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• Resumen

  • We consider those Hausdorff spaces that are the continuous image of some compact ordered space. Utilizing a theorem of Treybig, we characterize those continuous images of compact ordered spaces that are metrizable. In doing so, we give a ''best possible" metrization theorem for separable images of compact ordered spaces. In particular, a Hausdorff space that is the continuous image of some compact ordered space is metrizable if and only it is separable and may be embedded as a G-delta subset of some locally connected continuum. We also obtain some corollaries and related results.