Combinatorial and topological games

Baire spaces and applications in classical mathematics

Lecture notes · José Iovino

© 2026 José Iovino. All rights reserved. Work in progress: please link to this page rather than posting copies.

Topological games characterize Baire spaces and complete metrizability, and, with their rules changed, settle problems across mathematics; an epilogue tells the story of the Scottish Book.

• The notes are a work in progress, so I (JI) would love to hear your suggestions for improvement PDF

topologyBaire categorytopological gamesBanach–Mazur gameChoquet gameSchmidt gamemetric number theoryhomogeneous dynamicscomputational complexityRamsey theoryBanach spacestopological groups