کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
9516957 | 1633127 | 2005 | 11 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Compactness of certain bounded zero-sets in completely regular spaces
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
هندسه و توپولوژی
پیش نمایش صفحه اول مقاله
چکیده انگلیسی
Let X be a completely regular T1-space. A zero-set Z in X is called a full zero-set if clβXZ is a zero-set in the Äech-Stone compactification βX of X. As an generalization of theorems by W.G. McArthur and V. V. Uspenskii, we prove that every bounded, full zero-set F in X is compact if either (i) X has a regular Gδ-diagonal or (ii) X is a Baire space such that every open cover has a Ï-point-finite open refinement. In case (i), F is metrizable by Å neıËder's theorem. We also apply this to show that if the Dieudonné completion μX of X is a paracompact M-space, then X is metrizable if either (i) or (iii) X is a Baire space with a Ï-point-finite base.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Topology and its Applications - Volume 148, Issues 1â3, 28 February 2005, Pages 153-163
Journal: Topology and its Applications - Volume 148, Issues 1â3, 28 February 2005, Pages 153-163
نویسندگان
Lei Mou,