Unbounded towers and the Michael line topology

2022/09/07 by Wanda Przybylska, Przybylska, Wanda
Computer Science · Mathematics · #Advanced Topology and Set Theory #Computability, Logic, AI Algorithms #FOS: Mathematics #General Topology (math.GN) #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.2209.03130

openalex publication_date 2022/09/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A topological space satisfies \GNga (also known as Gerlits--Nagy's property γ) if every open cover of the space such that each finite subset of the space is contained in a member of the cover, contains a point-cofinite cover of the space. A topological space satisfies \ctblga if in the above definition we consider countable covers. We prove that subspaces of the Michael line with a special combinatorial structure have the property \ctblga. Then we apply this result to products of sets of reals with the property \GNga. The main method used in the paper is coherent omission of intervals invented by Tsaban.

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