کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4660374 1344365 2010 11 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
A glance at spaces with closure-preserving local bases
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات هندسه و توپولوژی
پیش نمایش صفحه اول مقاله
A glance at spaces with closure-preserving local bases
چکیده انگلیسی

Call a space X (weakly) Japanese at a point x∈X if X has a closure-preserving local base (or quasi-base respectively) at the point x. The space X is (weakly) Japanese if it is (weakly) Japanese at every x∈X. We prove, in particular, that any generalized ordered space is Japanese and that the property of being (weakly) Japanese is preserved by σ-products; besides, a dyadic compact space is weakly Japanese if and only if it is metrizable. It turns out that every scattered Corson compact space is Japanese while there exist even Eberlein compact spaces which are not weakly Japanese. We show that a continuous image of a compact first countable space can fail to be weakly Japanese so the (weak) Japanese property is not preserved by perfect maps. Another interesting property of Japanese spaces is their tightness-monolithity, i.e., in every weakly Japanese space X we have for any set A⊂X.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Topology and its Applications - Volume 157, Issue 3, 15 February 2010, Pages 548-558