2019/03/19 by Samuele Mongodi, Mongodi, Samuele · 1 citation
Mathematics · #Advanced Operator Algebra Research #Complex Variables (math.CV) #FOS: Mathematics #Geometric and Algebraic Topology #Holomorphic and Operator Theory
paper · pdf · doi:10.48550/arxiv.1903.08104
openalex publication_date 2019/03/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this short note, we collect some results regarding the Remmert reduction of holomorphically convex space and its application to a variation of the usual union problem. Classically, the union problem asks the following question: is a complex space, which is an increasing union of Stein subspaces X1\Subset X2\Subset⋯, a Stein space itself? The variation we are interested in is the following: is a complex space, which is an increasing union of holomorphically convex subspaces X1\Subset X2\Subset⋯, holomorphically convex itself? The results presented here are close analogues of (some of) those alredy present in the literature for the Stein case; our aim is only to collect such material for reference, as we consider it well known.