کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4658514 | 1633098 | 2015 | 17 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
F-Dugundji spaces, F-Milutin spaces and absolute F-valued retracts
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
هندسه و توپولوژی
پیش نمایش صفحه اول مقاله
چکیده انگلیسی
For every functional functor F:CompâComp in the category Comp of compact Hausdorff spaces we define the notions of F-Dugundji and F-Milutin spaces, generalizing the classical notions of Dugundji and Milutin spaces. We prove that the class of F-Dugundji spaces coincides with the class of absolute F-valued retracts. Next, we show that for a monomorphic continuous functor F:CompâComp admitting tensor products each Dugundji compact space is an absolute F-valued retract if and only if the doubleton {0,1} is an absolute F-valued retract if and only if some points aâF({0})âF({0,1}) and bâF({1})âF({0,1}) can be linked by a continuous path in F({0,1}). We prove that for the functor Lipk of k-Lipschitz functionals with k<2, each absolute Lipk-valued retract is openly generated. On the other hand, the one-point compactification of any uncountable discrete space is not openly generated but is an absolute Lip3-valued retract. More generally, each hereditarily paracompact scattered compact space X of finite scattered height n=ht(X) is an absolute Lipk-valued retract for k=2n+2â1.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Topology and its Applications - Volume 179, 1 January 2015, Pages 34-50
Journal: Topology and its Applications - Volume 179, 1 January 2015, Pages 34-50
نویسندگان
Taras Banakh, Taras Radul,