The Quillen model category of topological spaces

TL;DR

This paper provides a detailed proof of Quillen's theorem establishing the standard model category structure on topological spaces, making the concept accessible without prior knowledge of model categories.

Contribution

It offers a comprehensive, accessible proof of the model category structure on topological spaces, filling gaps for readers unfamiliar with the framework.

Findings

Confirmed the existence of the standard model structure on topological spaces

Provided a detailed, accessible proof of Quillen's theorem

Clarified foundational aspects of model categories in topology

Abstract

We give a complete and careful proof of Quillen's theorem on the existence of the standard model category structure on the category of topological spaces. We do not assume any familiarity with model categories.