کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4661018 1633120 2008 6 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Symmetric and tufted assignments of neighbourhoods and metrization
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات هندسه و توپولوژی
پیش نمایش صفحه اول مقاله
Symmetric and tufted assignments of neighbourhoods and metrization
چکیده انگلیسی

We identify the concept of a tufted assignment of neighbourhoods and with it strengthen a remarkable theorem of Nagata to have: Every metrizable space has a metric with respect to which balls of equal radii constitute a tufted and symmetric assignment of neighbourhoods. We also have: The availability on a T3-space of a basic sequence of tufted and symmetric assignments of neighbourhoods is (necessary and) sufficient for metrizability. Hausdorff spaces are paracompact if and only if open covers have refinements in the form of tufted and symmetric assignments of neighbourhoods. Moore spaces X are metrizable if (and only if) given any open cover W, there is such a sequence of tufted and symmetric assignment of neighbourhoods that, for every x∈X, Un(x)⊂St(x,W) for some n. T3-spaces are strongly metrizable if and only if on them there are basic sequences of symmetric, point-finite assignments of neighbourhoods.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Topology and its Applications - Volume 155, Issues 17–18, 15 October 2008, Pages 2137-2142