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 gro...

A topological space $X$ is defined to have a neighborhood $P$-base at any $x\in X$ from some partially ordered set (poset) $P$ if there exists base $(U_p[x])_{p\in P}$ $x$ such that $U_p[x]\subseteq U_{p’}[x]$ for all $p\geq p’$ in $P$. We prove compact countable, hence metrizable, it has countable scattered height and $\mathcal {K}(M)$-base separable metric $M$. Banakh [Dissertationes Math...