2022/10/14 by De-Xuan Hu, Hu, Dexuan, Sławomir Solecki +1
Mathematics · #Advanced Banach Space Theory #Advanced Topics in Algebra #Commutative Algebra (math.AC) #FOS: Mathematics #Logic (math.LO) #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.2210.07989
openalex publication_date 2022/10/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
We give a method of producing a Polish module over an arbitrary subring of \mathbb Q from an ideal of subsets of \mathbb N and a sequence in \mathbb N. The method allows us to construct two Polish \mathbb Q-vector spaces, U and V, such that -- both U and V embed into \mathbb R but -- U does not embed into V and V does not embed into U, where by an embedding we understand a continuous \mathbb Q-linear injection. This construction answers a question of Frisch and Shinko. In fact, our method produces a large number of incomparable with respect to embeddings Polish \mathbb Q-vector spaces.