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By Agata (i-napl) Di Maio, G. [di Maio, Lj. D. R. [kočinac, Ljubiˇsa D. R. (se-nissm, L. Babinkostova, C. Guido, Lj. D. R. Kočinac and M. Scheepers


MR1472172 (98k:54035)] introduced the following definitions: 1. A space X is an (a)-space if for each open cover U of X and each dense subset D of X there is a closed discrete (in X) set A ⊂ D such that st(A, U) = X. 2. A space X is a (pp)-space if for each open cover U of X there is an open refinement V of U such that if xV ∈ V for each V ∈ V, then the set {xV |V ∈ V} is a closed discrete set in X. The authors of the paper under review have been studying selection principles. A typical selection principle would be the following: Suppose that U and B are collections of open covers of a space X. The selection principle Slf(U, B) is the statement that for each sequence 〈Un: n ∈ ω 〉 of elements of U there is a sequence 〈Vn: n ∈ ω 〉 such that for each n, Vn is a locally finite open refinement of Un and ⋃ n∈ω Vn ∈ B. In this paper, the authors introduce selection principle versions of the (a)-space and (pp)space conditions and study these properties in connection with preservation results with respect to products, continuous images, formation of Aleksandrov duplicates, and so on. A number of interesting results are obtained

Topics: Topology (II, Metacompactness, unpublished notes, 2001
Year: 2013
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