| In this paper the preimage problem and hereditarily of θ-refinability are discussed.The main results are as followsi (1) The preimage of weakly δθ-refinable (δθ-refinable, weakly θ-refinable) space under a continuous closed mapping with f-1(y) Lindelof is weakly δθ-refinable (δθ-refinable, weakly θ-refinable) space; (2) The θ-refinable space with closed Gδ is a hereditarily θ-refinable space. |
