کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4661366 | 1344425 | 2007 | 4 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Covering compacta by discrete subspaces
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
هندسه و توپولوژی
پیش نمایش صفحه اول مقاله
چکیده انگلیسی
For any space X, denote by dis(X) the smallest (infinite) cardinal κ such that κ many discrete subspaces are needed to cover X. It is easy to see that if X is any crowded (i.e. dense-in-itself) compactum then dis(X)⩾m, where m denotes the additivity of the meager ideal on the reals. It is a natural, and apparently quite difficult, question whether in this inequality m could be replaced by c. Here we show that this can be done if X is also hereditarily normal.Moreover, we prove the following mapping theorem that involves the cardinal function dis(X). If is a continuous surjection of a countably compact T2 space X onto a perfect T3 space Y then .
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Topology and its Applications - Volume 154, Issue 2, 15 January 2007, Pages 283-286
Journal: Topology and its Applications - Volume 154, Issue 2, 15 January 2007, Pages 283-286