We prove a generalization of Thom’s transversality theorem. It gives conditions under which the jet map f∗|Y : Y ⊆ Jr(D,M)→ Jr(D,N) is generically (for f : M → N) transverse to a submanifold Z ⊆ Jr(D,N). We apply this to study transversality properties of a restriction of a fixed map g : M → P to the preimage (jsf)−1(A) of a submanifold A ⊆ Js(M,N) in terms of transversality properties of the o...

We introduce a new topological semantics for belief logics in which the belief modality is interpreted as the interior of the closure of the interior operator. We show that the system wKD45, a weakened version of KD45, is sound and complete w.r.t. the class of all topological spaces. Moreover, we point out a problem regarding updates on extremally disconnected spaces that appears in the setting...

Abstract Let G be a countably infinite discrete amenable group. It should noted that -system $(X,G)$ naturally induces $(\mathcal {M}(X),G)$ , where $\mathcal {M}(X)$ denotes the space of Borel probability measures on compact metric X endowed with weak*-topology. A factor map $\pi : (X,G)\to (Y,G)$ between two -systems $\widetilde {\pi }:(\mathcal {M}(X),G)\to (\mathcal {M}(Y),G)$ . turns out }...

Let M⊂B(H) be a von Neumann algebra acting on the (separable) Hilbert space H. We first prove that M is finite if and only if, for every x∈M all vectors ξ,η∈H, coefficient function u↦⟨uxu∗ξ|η⟩ weakly almost periodic topological group UM of unitaries in (equipped with weak operator topology). The main device unique invariant mean C∗-algebra WAP(UM) functions UM. Next, we direct sum diffuse, abel...