کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
8904637 | 1633753 | 2018 | 15 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
A compact minimal space Y such that its square Yâ¯Ãâ¯Y is not minimal
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
ریاضیات (عمومی)
پیش نمایش صفحه اول مقاله
چکیده انگلیسی
The following well known open problem is answered in the negative: Given two compact spaces X and Y that admit minimal homeomorphisms, must the Cartesian product XÃY admit a minimal homeomorphism as well? Moreover, it is shown that such spaces can be realized as minimal sets of torus homeomorphisms homotopic to the identity. A key element of our construction is an inverse limit approach inspired by combination of a technique of Aarts & Oversteegen and the construction of Slovak spaces by Downarowicz & Snoha & Tywoniuk. This approach allows us also to prove the following result. Let Ï:MÃRâM be a continuous, aperiodic minimal flow on the compact, finite-dimensional metric space M. Then there is a generic choice of parameters câR, such that the homeomorphism h(x)=Ï(x,c) admits a noninvertible minimal map f:MâM as an almost 1-1 extension.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Advances in Mathematics - Volume 335, 7 September 2018, Pages 261-275
Journal: Advances in Mathematics - Volume 335, 7 September 2018, Pages 261-275
نویسندگان
J.P. BoroÅski, Alex Clark, P. Oprocha,