Note on the quasi-proper direct image with value in a Banach analytic set

TL;DR

This paper provides a simplified proof of the generalized quasi-proper direct image theorem for maps into Banach analytic sets, extending classical results using a generalized Remmert-Stein theorem.

Contribution

It introduces a straightforward proof of the quasi-proper direct image theorem for Banach analytic sets, broadening the scope of classical complex analytic results.

Findings

Generalization of Kuhlmann's theorem to Banach analytic sets

Use of a generalized Remmert-Stein theorem in the proof

Simplification of the proof process

Abstract

We give a rather simple proof of the generalization of Kuhlmann's quasi-proper direct image theorem to the case of a map with values in a Banach analytic set. The proof uses a generalization of the Remmert-Stein's theorem to this context. AMS Classification. 32 H 02-32 K 05-32 C 25.