Condensations onto connected metrizable spaces

• Autores: Irina Druzhinina
• Localización: Houston journal of mathematics, ISSN 0362-1588, Vol. 30, Nº 3, 2004, págs. 751-766
• Idioma: inglés
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• Resumen

  • We study when a metrizable space X has a weaker connected metrizable topology and prove that:

    (a) if the weight of X is less than or equal to the continuuum, then X admits a weaker connected separable metrizable topology whenever X contains a closed subspace which condenses onto a connected non-compact metrizable space;

    (b) if the weight of X is greater than or equal to the continuum, then X admits a weaker connected metrizable topology whenever X contains a closed discrete subset of cardinality equal to its weight. It is also established that if Y is a sigma-discrete or a closed subset of a connected metrizable space X, then the complement X\Y condenses onto a connected metrizable space.