A converse of Cartan's Theorem B for Real Analytic Set

TL;DR

This paper proves a converse to Cartan's Theorem B specifically for real analytic sets, extending classical complex analytic results to the real setting.

Contribution

It establishes a new converse theorem for Cartan's Theorem B in the context of real analytic sets, previously known only in complex analysis.

Findings

Proves a converse to Cartan's Theorem B for real analytic sets

Extends classical complex theorems to real analytic geometry

Provides foundational results for real analytic set theory

Abstract

In this lecture we prove a converse to Cartan's Theorem B for real analytic sets, due to Fernando and Ghiloni [arXiv:2506.18347].