کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4659948 1344343 2012 11 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Fragmentability of groups and metric-valued function spaces
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات هندسه و توپولوژی
پیش نمایش صفحه اول مقاله
Fragmentability of groups and metric-valued function spaces
چکیده انگلیسی

Let (X,τ) be a topological space and let ρ be a metric defined on X. We shall say that (X,τ) is fragmented by ρ if whenever ε>0 and A is a nonempty subset of X there is a τ-open set U such that U∩A≠∅ and ρ−diam(U∩A)<ε. In this paper we consider the notion of fragmentability, and its generalisation σ-fragmentability, in the setting of topological groups and metric-valued function spaces. We show that in the presence of Baireness fragmentability of a topological group is very close to metrizability of that group. We also show that for a compact Hausdorff space X, σ-fragmentability of (C(X),‖⋅‖∞) implies that the space Cp(X;M) of all continuous functions from X into a metric space M, endowed with the topology of pointwise convergence on X, is fragmented by a metric whose topology is at least as strong as the uniform topology on C(X;M). The primary tool used is that of topological games.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Topology and its Applications - Volume 159, Issue 1, 1 January 2012, Pages 183-193