کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4657815 1633069 2016 10 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
On metric spaces where continuous real valued functions are uniformly continuous in ZF
ترجمه فارسی عنوان
درباره فضاهای متریک که در آن توابع حقیقی مقدار پیوسته بصورت یکنواخت در ZF پیوسته هستند
کلمات کلیدی
اصل انتخاب؛ توالی Cofinally کوشی؛ فشرده؛ فشرده قابل شمارش؛ فشرده متوالی؛ کامل؛ فضاهای متریک کاملا محدود و Lebesgue
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات هندسه و توپولوژی
چکیده انگلیسی

We show that the negation of each one of the following statements is consistent with ZF:(i) Every sequentially compact metric space X=(X,d)X=(X,d) is normal, i.e., the distance of any two disjoint non-empty closed subsets of X is strictly positive.(ii) If (X,d)(X,d) is a sequentially compact metric space then X is a UC space, i.e., every continuous real valued on X is uniformly continuous.(iii) If (X,d)(X,d) is a UC metric space then X is Lebesgue, i.e., every open cover of X has a Lebesgue number.(iv) If (X,d)(X,d) is a metric space such that every countable open cover of X has a Lebesgue number then X is Lebesgue.We also show:(v) For every metric space X, the following are equivalent:(1) Every sequence in X admits a Cauchy subsequence;(2) For every sequence (xn)n∈N(xn)n∈N of X, for each ε>0ε>0 there is an infinite Nε⊆NNε⊆N such that d(xn,xm)<εd(xn,xm)<ε whenever n,m∈Nεn,m∈Nε;(3) For every sequence (xn)n∈N(xn)n∈N of X, for each ε>0ε>0 and for each n0∈Nn0∈N there exist n,m∈Nn,m∈N, n,m≥n0n,m≥n0, n≠mn≠m such that d(xn,xm)<εd(xn,xm)<ε.(vi) The axiom of countable choice CAC implies that for every metric space X the following statements are equivalent:(1) X is Lebesgue;(2) Every countable open cover of X has a Lebesgue number;(3) X is UC.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Topology and its Applications - Volume 210, 1 September 2016, Pages 366–375
نویسندگان
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