کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4659508 1344326 2012 7 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Strongly non-embeddable metric spaces
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات هندسه و توپولوژی
پیش نمایش صفحه اول مقاله
Strongly non-embeddable metric spaces
چکیده انگلیسی

Enflo (1969) [4], constructed a countable metric space that may not be uniformly embedded into any metric space of positive generalized roundness. Dranishnikov, Gong, Lafforgue and Yu (2002) [3] modified Enfloʼs example to construct a locally finite metric space that may not be coarsely embedded into any Hilbert space. In this paper we meld these two examples into one simpler construction. The outcome is a locally finite metric space (Z,ζ) which is strongly non-embeddable in the sense that it may not be embedded uniformly or coarsely into any metric space of non-zero generalized roundness. Moreover, we show that both types of embedding may be obstructed by a common recursive principle. It follows from our construction that any metric space which is Lipschitz universal for all locally finite metric spaces may not be embedded uniformly or coarsely into any metric space of non-zero generalized roundness. Our construction is then adapted to show that the group Zω=⊕ℵ0Z admits a Cayley graph which may not be coarsely embedded into any metric space of non-zero generalized roundness. Finally, for each p⩾0 and each locally finite metric space (Z,d), we prove the existence of a Lipschitz injection f:Z→ℓp.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Topology and its Applications - Volume 159, Issue 3, 15 February 2012, Pages 749-755