کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4658208 | 1633083 | 2015 | 8 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
On topological groups with a first-countable remainder, II
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
هندسه و توپولوژی
پیش نمایش صفحه اول مقاله
چکیده انگلیسی
We establish estimates on cardinal invariants of an arbitrary non-locally compact topological group G with a first-countable remainder Y. We show that the weight of G and the cardinality of Y do not exceed 2Ï. Moreover, the cardinality of G does not exceed 2Ï1. These bounds are best possible as witnessed by a single topological group G. We also prove that every precompact topological group with a first-countable remainder is separable and metrizable. It is known that under Martin's Axiom and the negation of the Continuum Hypothesis, every Ï-compact topological group with a first-countable remainder is metrizable. We show that under the Continuum Hypothesis, there is an example of a countable topological group which is not metrizable and has a first-countable remainder. Hence for countable groups, the question of whether the existence of a first-countable remainder is equivalent to being metrizable, is undecidable.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Topology and its Applications - Volume 195, November 2015, Pages 143-150
Journal: Topology and its Applications - Volume 195, November 2015, Pages 143-150
نویسندگان
A.V. Arhangel'skii, J. van Mill,