Correction and strengthening of "How large are the level sets of the Takagi function?"

TL;DR

This paper corrects an earlier error regarding the Takagi function's level sets and proves a stronger result about the prevalence of uncountably many local level sets within them.

Contribution

It provides a correction to previous work and establishes a more robust result on the structure of level sets of the Takagi function.

Findings

Corrects an earlier error in Takagi function level set analysis

Proves a stronger form of the main result about uncountably many local level sets

Enhances understanding of the structure of Takagi function level sets

Abstract

The purpose of this note is to correct an error in an earlier paper by the author about the level sets of the Takagi function [Monatsh. Math. 167 (2012), 311-331 and arXiv:1102.1616], and to prove a stronger form of one of the main results of that paper about the propensity of level sets containing uncountably many local level sets.