English

Union of holomorphically convex spaces

Complex Variables 2019-03-20 v1

Abstract

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 X1X2X_1\Subset X_2\Subset\cdots, 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 X1X2X_1\Subset X_2\Subset\cdots, 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.

Keywords

Cite

@article{arxiv.1903.08104,
  title  = {Union of holomorphically convex spaces},
  author = {Samuele Mongodi},
  journal= {arXiv preprint arXiv:1903.08104},
  year   = {2019}
}
R2 v1 2026-06-23T08:13:03.673Z