کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4658211 | 1633083 | 2015 | 13 صفحه PDF | دانلود رایگان |
Given a property P of subspaces of a T1T1 space X, we say that X is P-bounded iff every subspace of X with property P has compact closure in X. Here we study P -bounded spaces for the properties P∈{ωD,ωN,C2}P∈{ωD,ωN,C2} where ωD ≡ “countable discrete”, ωN ≡ “countable nowhere dense”, and C2C2 ≡ “second countable”. Clearly, for each of these P-bounded is between countably compact and ω-bounded.We give examples in ZFC that separate all these boundedness properties and their appropriate combinations. Consistent separating examples with better properties (such as: smaller cardinality or weight, local compactness, first countability) are also produced.We have interesting results concerning ωD-bounded spaces which show that ωD-boundedness is much stronger than countable compactness:
• Regular ωD -bounded spaces of Lindelöf degree
• If a product of Hausdorff spaces is ωD-bounded then all but one of its factors must be ω-bounded.
• Any product of at most tt many ωD-bounded spaces is countably compact.As a byproduct we obtain that regular, countably tight, and countably compact spaces are discretely generated.
Journal: Topology and its Applications - Volume 195, November 2015, Pages 196–208