Abstract
In this paper, we define near-compact mappings and characterize the sequence-covering, near-compact images of metric spaces. The following main result is obtained. The following are equivalent for a space X:(1) X is a 1-sequence-covering near-compact image of a metric space.(2) X is a sequence-covering near-compact image of a metric space.(3) X has a sequence of cs-covers which is a point-finite point-star network at NS(X).(4) X has a sequence of sn-covers which is a point-finite point-star network at NS(X).
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