The Isotropy Group for the Topos of Continuous G-Sets

Abstract

The objective of this thesis is to provide a detailed analysis of a new invariant for Grothendieck topoi in the special case of the topos of continuous G-sets and continuous G-equivariant maps. We use a well-known site to present the isotropy group in elementary terms, as systems of right cosets of open subgroups of G. We establish properties of the the isotropy group for an arbitrary topological group and use the developed theory to compute the isotropy group for the Schanuel topos.