کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
5777881 | 1633052 | 2017 | 20 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
The strong Pytkeev property in topological spaces
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
هندسه و توپولوژی
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چکیده انگلیسی
A topological space X has the strong Pytkeev property at a point xâX if there exists a countable family N of subsets of X such that for each neighborhood OxâX and subset AâX accumulating at x, there is a set NâN such that NâOx and Nâ©A is infinite. We prove that for any âµ0-space X and any space Y with the strong Pytkeev property at a point yâY the function space Ck(X,Y) has the strong Pytkeev property at the constant function Xâ{y}âY. If the space Y is rectifiable, then the function space Ck(X,Y) is rectifiable and has the strong Pytkeev property at each point. We also prove that for any pointed spaces (Xn,ân), nâÏ, with the strong Pytkeev property their Tychonoff product ânâÏXn and their small box-product â¡nâÏXn both have the strong Pytkeev property at the distinguished point (ân)nâÏ. We prove that a sequential rectifiable space X has the strong Pytkeev property if and only if X is metrizable or contains a clopen submetrizable kÏ-subspace. A locally precompact topological group is metrizable if and only if it contains a dense subgroup with the strong Pytkeev property.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Topology and its Applications - Volume 227, 15 August 2017, Pages 10-29
Journal: Topology and its Applications - Volume 227, 15 August 2017, Pages 10-29
نویسندگان
Taras Banakh, Arkady Leiderman,