Submaximal spaces and cardinal invariants

2021/12/07 by Corral, César
Computer Science · Mathematics · Psychology · #03E17 #03E35 #54A25 #54A35 #Advanced Topology and Set Theory #Computability, Logic, AI Algorithms #FOS: Mathematics #General Topology (math.GN) #Logic (math.LO) #Philosophy and Theoretical Science

paper · pdf · doi:10.48550/arxiv.2112.03447

openalex publication_date 2021/12/07 · openalex created_date 2022/05/05 · openalex updated_date 2026/07/28

Abstract

We give a combinatorial characterization of countable submaximal subspaces of 2^κ. Using a parametrized version of Mathias forcing, we prove that there exists a countable submaximal subspace of 2^ω₁ whilst \mathfrakc=ω₂. Combining this with previous results, we construct a disjointly tight countable irresolvable space of weight

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