Keita Yokoyama - Reverse mathematics for analysis: an introduction, Lecture 3

This lecture was part of the Summer School on "Reverse Mathematics: New Paradigms." held at the ESI July 28 - August 1, 2025. In this course, we will start by reviewing the "big five" and other subsystems of second-order arithmetic, along with their basic properties. Then, we will establish the definitions of open/closed sets and continuous functions for Polish spaces. With these set-ups, we will study in some reverse mathematics for basic analysis. If time permits, we will extend the definitions of functions on Polish spaces to explore additional topics in analysis.