On compact-covering and sequence-covering images of metric spaces (Q2853271)

To find internal characterizations of certain images of metric spaces is one of the central problems in general topology. The compact-covering and open images of metric spaces are the first countable spaces every compact subset of which is metrizable. However, the inverse does not hold and thus one wants to know for first countable spaces every compact subset of which is metrizable, how to characterize them as certain images of metric spaces.NEWLINENEWLINE The author studies the characterizations of compact-covering and 1-sequence-covering (resp. 2-sequence-covering) images of metric spaces and gives a positive answer to the above question.