کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4657800 1633069 2016 36 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
A reconstruction theorem for locally convex metrizable spaces, homeomorphism groups without small sets, semigroups of non-shrinking functions of a normed space
ترجمه فارسی عنوان
یک قضیه بازسازی برای فضاهای قابل متراکم محاسبه محلی، گروه های هومومورفیسم بدون مجموعه های کوچک، نیمه گروهی از توابع ناپایدار یک فضای معمولی
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات هندسه و توپولوژی
چکیده انگلیسی

Definition. Let X be a topological space and G   be a subgroup of the group H(X)H(X) of all auto-homeomorphisms of X  . The pair (X,G)(X,G) is then called a space-group pair. Let K be a class of space-group pairs. K is called a faithfull class   if for every (X,G),(Y,H)∈K(X,G),(Y,H)∈K and an isomorphism φ between the groups G and H there is a homeomorphism τ between X and Y   such that φ(g)=τ∘g∘τ−1φ(g)=τ∘g∘τ−1 for every g∈Gg∈G.Theorem 1. The class  K:={(X,H(X))|X is a nonempty open subset of ametrizable locally convex topological vector space E}is faithful.Definition. Let (X,G)(X,G) be a space-group pair and ∅≠U⊆X∅≠U⊆X be open. We say that U is a small set   with respect to (X,G)(X,G), if for every open nonempty V⊆UV⊆U there is g∈Gg∈G such that g(U)⊆Vg(U)⊆V.Remarks. (a) We do not know whether the members of K have small sets.(b) Earlier faithfulness theorems, required the existence of small sets.Theorem 2. Let N be the class of all spaces X such that for some normed space  E≠{0}E≠{0}, X is a nonempty open subset of E. For every  X∈NX∈Nthere is a subgroup  GX⊆H(X)GX⊆H(X)such that: (1)  (X,GX)(X,GX)has no small sets, and (2)  {(X,GX)|X∈N}is faithful.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Topology and its Applications - Volume 210, 1 September 2016, Pages 97–132
نویسندگان
, ,