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Spaces with countable s n -networks

Ge Ying (2004)

Commentationes Mathematicae Universitatis Carolinae

In this paper, we prove that a space X is a sequentially-quotient π -image of a metric space if and only if X has a point-star s n -network consisting of c s * -covers. By this result, we prove that a space X is a sequentially-quotient π -image of a separable metric space if and only if X has a countable s n -network, if and only if X is a sequentially-quotient compact image of a separable metric space; this answers a question raised by Shou Lin affirmatively. We also obtain some results on spaces with countable...

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