John (Ted) E. Porter, Ph.D. is this week’s #RacerScholar

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.

Abstract

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.

1-s2-0-s0166864115x00137-cov150hThe 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
DOI: 10.1016/j.topol.2015.08.007

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