Some properties of almost contra-precontinuous functions.
In this paper, we prove that a space is a sequentially-quotient -image of a metric space if and only if has a point-star -network consisting of -covers. By this result, we prove that a space is a sequentially-quotient -image of a separable metric space if and only if has a countable -network, if and only if 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...