On (non-Menger) spaces whose closed nowhere dense subsets are Menger

2025/01/22 by Mathieu Baillif, Baillif, Mathieu, Santi Spadaro +1 · 1 voice
Mathematics · #54D20 #FOS: Mathematics #General Topology (math.GN) #math.GN

paper · pdf · doi:10.48550/arxiv.2501.13220

Abstract

A space X is od-Menger if it satisfies \mathsfU_fin(Δ_X, O_X), where O_X,Δ_X are the collection of covers of X by respectively open subsets and open dense subsets. We show that under CH, there is a refinement of the usual topology on a subset of the reals which yields a hereditarily Lindelöf, od-Menger, non-Menger, 0-dimensional, first countable space. We also investigate the properties of spaces which are od-Menger but not Menger.

Discussions

• Mathieu Baillif, Santi Spadaro: On (non-Menger) spaces whose closed nowhere dense subsets are Menger https://arxiv.org/abs/2501.13220 https://arxiv.org/pdf/2501.13220 https://arxiv.org/html/2501.13220 [bsky, 0 points, 1 comments]

Related

• A 0-dimensional, Lindelöf space that is not strongly D
• Definable versions of Menger's conjecture
• Totally paracompact spaces and the Menger covering property
• The Menger and projective Menger properties of function spaces with the set-open topology
• Products of general Menger spaces