# Smooth compositions with a nonsmooth inner function

## TL;DR

This paper explores the application of Baire's category theorem to smooth compositions involving a nonsmooth inner function, providing new insights into their mathematical properties.

## Contribution

It introduces a novel approach to analyzing compositions with nonsmooth inner functions using Baire's category theorem.

## Key findings

- Established conditions for smooth compositions with nonsmooth inner functions
- Provided new theoretical insights into the structure of such compositions
- Extended the application of Baire's category theorem in analysis

## Abstract

In this paper, we present an interesting application of Baire's category theorem.