کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
9516824 | 1344436 | 2005 | 11 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Note on separate continuity and the Namioka property
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
هندسه و توپولوژی
پیش نمایش صفحه اول مقاله
چکیده انگلیسی
A pair ãB,Kã is a Namioka pair if K is compact and for any separately continuous f:BÃKâR, there is a dense AâB such that f is (âjointly) continuous on AÃK. We give an example of a Choquet space B and separately continuous f:BÃβBâR such that the restriction f|Î to the diagonal does not have a dense set of continuity points. However, for K a compact fragmentable space we have: For any separately continuous f:TÃKâR and for any Baire subspace F of TÃK, the set of points of continuity of f|F:FâR is dense in F. We say that ãB,Kã is a weak-Namioka pair if K is compact and for any separately continuous f:BÃKâR and a closed subset F projecting irreducibly onto B, the set of points of continuity of f|F is dense in F. We show that T is a Baire space if the pair ãT,Kã is a weak-Namioka pair for every compact K. Under (CH) there is an example of a space B such that ãB,Kã is a Namioka pair for every compact K but there is a countably compact C and a separately continuous f:BÃCâR which has no dense set of continuity points; in fact, f does not even have the Baire property.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Topology and its Applications - Volume 152, Issue 3, 14 July 2005, Pages 258-268
Journal: Topology and its Applications - Volume 152, Issue 3, 14 July 2005, Pages 258-268
نویسندگان
Dennis K. Burke, Roman Pol,