The Collins-Roscoe structuring mechanism, D-spaces and related topics

摘要

We study the relationship between the Collins-Roscoe structuring mechanism and D-spaces. We introduce the notion of k-sheltering and sigma-sheltering point networks. We show that sigma-sheltering (F) spaces are D-spaces which improves the results of Gruenhage and Yuming, and also show that Sigma*-products of sigma-sheltering (F) spaces are also sigma-sheltering spaces. In addition, we show that omega(1)-sheltering (F) spaces are D-sigma-spaces and transitively D-spaces. As a corollary, monotonic