General Group Actions

This lecture covers the construction of group actions on vector spaces and topological spaces, exploring the definition of the 'fixed points' functor from the category of topological G-spaces to the category of topological spaces. It also delves into the relationships between different functors connecting categories, such as the links between Ens and Ens. The lecture further discusses free actions, orbits, and points fixes, providing examples of non-trivial actions of C₂ on various spaces. Additionally, it examines how group actions can be viewed as actions on topological spaces, emphasizing the importance of understanding morphisms in the context of topological spaces.