کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
9516952 | 1633127 | 2005 | 20 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Embeddability properties of countable metric spaces
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
هندسه و توپولوژی
پیش نمایش صفحه اول مقاله
چکیده انگلیسی
For subspaces X and Y of Q the notation X⩽hY means that X is homeomorphic to a subspace of Y and Xâ¼Y means X⩽hY⩽hX. The resulting set P(Q)/â¼ of equivalence classes X¯={YâQ:Yâ¼X} is partially-ordered by the relation X¯⩽hY¯ if X⩽hY. It is shown that (P(Q),⩽h) is partially well-ordered in the sense that it lacks infinite anti-chains and infinite strictly descending chains. A characterization of (P(Q),⩽h) in terms of scattered subspaces of Q with finite Cantor-Bendixson rank is given and several results relating Cantor-Bendixson rank to this embeddability ordering are established. These results are obtained by studying a local homeomorphism invariant (type) for countable scattered metric spaces.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Topology and its Applications - Volume 148, Issues 1â3, 28 February 2005, Pages 63-82
Journal: Topology and its Applications - Volume 148, Issues 1â3, 28 February 2005, Pages 63-82
نویسندگان
W.D. Gillam,