کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
5777694 | 1633047 | 2017 | 28 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Iterations of Stone-Äech remainders
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
هندسه و توپولوژی
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چکیده انگلیسی
Consider a compact space X=L0âªL1 which is a disjoint union of two Lindelöf dense subsets L0, L1, and fix this partition. Then we repeat taking remainders of Stone-Äech compactifications Ï1 many times to construct a compact space Ω(X) which is “minimal” w.r.t. the property that Ω(X) admits an irreducible map Ï onto X such that both Ïâ1(L0) and Ïâ1(L1) are Câ-embedded in Ω(X). A typical example is the closed interval [0,1]=QâªP with the partition into the rationals Q and the irrationals P, and we can show that the resultant compact space Ω([0,1]) is not extremally disconnected, hence different from the absolute of [0,1]. We respond to one of van Douwen's questions in [2] that the length of iteration needed for Ω([0,1]) is the first uncountable ordinal Ï1.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Topology and its Applications - Volume 232, 1 December 2017, Pages 70-97
Journal: Topology and its Applications - Volume 232, 1 December 2017, Pages 70-97
نویسندگان
Akio Kato,