A remark on Fremlin-Miller theorem concerning the Menger property and Michael concentrated sets

Abstract

The theorem we prove is a slight strengthening of some results by Just, Miller, Scheepers and Szeptycki [JMSS]. We use the Michael technique instead of the combinatorial approach in the literature. Comments by the submitter: This short unpublished paper, written in 2002, is a cornerstone in the study of selection principles and classic covering properties. It is the first to solve the Hurewicz Problem, by showing that there is, in ZFC, a real set with Menger's covering property (indeed, in all finite powers) but without Hurewicz's covering property. Unfortunately, web searches begin to miss this paper, and I sought, and received, permission from the authors to store this paper in the ArXiv, providing it a permanent link. The author's decision to not publish this paper, in light of some later stronger results by other authors (including myself), is a true act of generosity. Hopefully, this submission does some justice to their achievement.