Skew-amenability of topological groups

We study skew-amenable topological groups, i.e., those admitting a left-invariant mean on the space of bounded real-valued functions left-uniformly continuous in sense Bourbaki. prove characterizations skew-amenability for groups isometries and automorphisms, clarify connection with extensive amenability group actions, establish Følner-type characterization, discuss closure properties class groups. Moreover, we isolate dynamical sufficient condition provide several concrete variations this criterion context transformation These results are then used to decide number examples built from or related Thompson’s $F$ Monod’s piecewise projective homeomorphisms real line.