Professor John E. Porter (Mathematics and Statistics) is this week’s #RacerScholar at Murray State University. Dr. Porter co-authored the paper, “The Collins-Roscoe structuring mechanism, D-spaces and related topics,” which appeared in the October 2015 issue of Topology and its Applications.
We study the relationship between the Collins–Roscoe structuring mechanism and D-spaces. We introduce the notion of κ-sheltering and σ-sheltering point networks. We show that σ-sheltering (F) spaces are D -spaces which improves the results of Gruenhage and Yuming, and also show that Σ⁎-products of σ-sheltering (F) spaces are also σ -sheltering spaces. In addition, we show that ω1-sheltering (F) spaces are Dσ-spaces and transitively D -spaces. As a corollary, monotonically normal ω1-sheltering (F) spaces are paracompact.
The Collins-Roscoe structuring mechanism,
D-spaces and related topics
By: Ziqin Feng and John E. Porter
Topology and its Applications, Oct. 2015,
vol. 194, pgs. 150-158