WebProperly discontinuous group actions (0.10) Recall that a group G acts continuously on X if for each g ∈ G there exists a homeomorphism ρ ( g): X → X such that ρ ( g h) = ρ ( g) ∘ ρ ( h) and ρ ( 1) = i d X. The quotient X / G is the set of equivalence classes, where x ∼ ρ ( g) x for all g ∈ G, equipped with the quotient topology. WebG が位相空間 X に作用する離散群であるとき、作用が固有不連続あるいは真性不連続 (properly discontinuous) であるのは、X の各点 x に対して開近傍 U が存在して、g(U) ∩ U ≠ ∅ となるような G の元 g 全体成す集合が、ただ一つ単位元のみからなるようにできる ...

general topology - Orbits of properly discontinuous actions ...

WebThis action is not properly discontinuous: If K is the unit circle cen- tered at the origin, then T n (K) intersects K for all n. • The action of SL 2 (Z) on the upper half plane discussed in … WebThe action of is free and properly discontinuous if and only if X= is a mani-fold quotient (Hausdorff) and X!X= is a covering map. a discrete subgroup of a Lie group Gacting on … phoenix australia definition of trauma

群作用 - Wikipedia

WebMeshes can be stabilized when properly dimensioned and arranged junctions and struts of the necessary properties are used. All of these stabilized fabrics can be made of synthetic polymer materials such as ultrahigh molecular weight PE or PP and expanded PTFE. ... On the other hand, a “discontinuous” suture line refers to a suture line ... WebThe action of a discrete subgroup Γ on M is not always properly discontinuous. In this paper, we give a criterion for properly discontinuous actions, which generalizes our previous work [6] for an analogous problem in the continuous setting. Furthermore, we introduce the discontinuous dual ⋔(H:G) of a subset H of G, and prove a duality ... phoenix auto body paint