Correction to : The Kuo condition, an inequality of Thom's type and (c)-regularity

TL;DR

This paper corrects a previous theorem on (c)-regularity, providing a weaker version that still supports the proof of related stratification theorems, ensuring mathematical rigor in stratification theory.

Contribution

It offers a corrected, weaker version of a key theorem on (c)-regularity, facilitating accurate proofs in stratification research.

Findings

A corrected theorem on (c)-regularity is presented.

The weaker version is sufficient for stratification proofs.

Ensures mathematical rigor in stratification conditions.

Abstract

We correct a statement of a theorem on characterisation of the (c)-regularity we gave in Topology 37 (1998), 45--62. This theorem was used in the paper in the proof of two theorems on the (c)-regular stratification. In this note we give a weaker version of the theorem as an alternative lemma which ensures the (c)-regularity condition and turn to be sufficient for the proof of the theorems.