In this paper, we study with uniform results the preimage of which the properties will preserve the same property under the continuous closed mapping whicd possess certain quite weak condition, for σ-metacompctness, θ-refinability, weakly θ-refinability, paralindel?fness, metalindelofness,δθ-refinability, weakly δθ-refinability, mesocompactness and sequentially mesocompactness, and so on. A necessary and sufficient condition about preimage problem, with uniform results, has been given in this paper; and therefore the results in D.K.Burke′s survey paper [4] have been strengthened in ihis paper. |