Resumen de Condensations onto connected metrizable spaces

Irina Druzhinina

• 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.