Point Set Topology is a Disease from Which the Human Race Will Soon Recover

This lecture by Professor M. Andrew Moshier from Chapman University explores locale theory as an alternative approach to point set topology, drawing from Poincaré's famous critique. Discover the foundations of locale theory, which conceptualizes space as a lattice of parts rather than collections of points. Learn how this framework, influenced by mathematicians like Ehresmann, Wallman, Stone, and Tarski, offers a different perspective where continuous functions operate on spatial parts while preserving their structure. The presentation begins with an accessible introduction to locales and their underlying intuitions, then demonstrates applications that are impossible within traditional point set frameworks, and concludes with recent developments in the field. Part of the Orange County Inland Empire Seminar series in History and Philosophy of Mathematics, this talk provides insights into an alternative mathematical approach to understanding topological spaces.