# Extension theorems of Sakai type for separately holomorphic and meromorphic functions

## TL;DR

This paper presents counterexamples to certain open questions about Sakai's theorem and establishes a new extension theorem for separately holomorphic and meromorphic functions, advancing the understanding of their extension properties.

## Contribution

It introduces an extension theorem of Sakai type for separately holomorphic and meromorphic functions, filling gaps in existing theory.

## Key findings

- Counterexamples to open questions in Sakai's theorem
- New extension theorem for separately holomorphic/meromorphic functions
- Enhanced understanding of extension properties in complex analysis

## Abstract

We first exhibit counterexamples to some open questions related to a theorem of Sakai. Then we establish an extension theorem of Sakai type for separately holomorphic/meromorphic functions.