کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
8904012 | 1633038 | 2018 | 8 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Quasi-metrizability of products in ZF and equivalences of CUT(fin)
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
هندسه و توپولوژی
پیش نمایش صفحه اول مقاله
چکیده انگلیسی
It is proved in ZF that if a collection of (quasi)-metric spaces is indexed by a countable union of finite sets, then the product of this collection is (quasi)-metrizable, while it is independent of ZF that every countable product of metrizable spaces is quasi-metrizable. It is also proved that if J is a non-empty set, while a space X, consisting of at least two points, is equipped with the co-finite topology, then the product XJ is quasi-metrizable if and only if both X and J are countable unions of finite sets. Several equivalences of CUT(fin) are deduced. It is shown that, in every model of ZF+¬CUT(fin), for an uncountable set J, the space NJ can be normal (even metrizable), a Cantor cube can be simultaneously metrizable, not second-countable and non-compact.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Topology and its Applications - Volume 241, 1 June 2018, Pages 62-69
Journal: Topology and its Applications - Volume 241, 1 June 2018, Pages 62-69
نویسندگان
Eliza Wajch,