کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
9516691 | 1633126 | 2005 | 15 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Dyadicity index and metrizability of compact continuous images of function spaces
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
هندسه و توپولوژی
پیش نمایش صفحه اول مقاله
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چکیده انگلیسی
We show that the dyadicity index can be increased by taking the square even in the class of second countable spaces. Besides, any compact group contains a dense subspace of dyadicity index zero. We prove that, for any infinite cardinal κ, a compact space K with Ï(x,K)⩾κ for any xâK cannot be represented as a union of ⩽κ-many subspaces of network weight <κ. This fact has quite a few interesting consequences when we consider mappings of function spaces onto compact spaces. We prove, in particular, that if K is an Ï1-monolithic Lindelöf Σ-space then every compact continuous image of Cp(K) is metrizable. For any cardinal κ an example is given of a compact space K such that Cp(K) maps continuously onto the Tychonoff cube of weight κ. We also establish that Luzin's axiom (2Ï1>c) is equivalent to metrizability of all compact continuous images of Cp(K) whenever K is a separable compact space.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Topology and its Applications - Volume 149, Issues 1â3, 28 April 2005, Pages 243-257
Journal: Topology and its Applications - Volume 149, Issues 1â3, 28 April 2005, Pages 243-257
نویسندگان
M.G. Tkachenko, V.V. Tkachuk,