کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4661491 | 1344431 | 2006 | 25 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
D-forced spaces: A new approach to resolvability
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
هندسه و توپولوژی
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چکیده انگلیسی
We introduce a ZFC method that enables us to build spaces (in fact special dense subspaces of certain Cantor cubes) in which we have “full control” over all dense subsets.Using this method we are able to construct, in ZFC, for each uncountable regular cardinal λ a 0-dimensional T2, hence Tychonov, space which is μ-resolvable for all μ<λ but not λ-resolvable. This yields the final (negative) solution of a celebrated problem of Ceder and Pearson raised in 1967: Are ω-resolvable spaces maximally resolvable? This method enables us to solve several other open problems concerning resolvability as well.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Topology and its Applications - Volume 153, Issue 11, 1 May 2006, Pages 1800-1824
Journal: Topology and its Applications - Volume 153, Issue 11, 1 May 2006, Pages 1800-1824