کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
6423532 1342400 2012 10 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Vertex partitions of metric spaces with finite distance sets
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات گسسته و ترکیبات
پیش نمایش صفحه اول مقاله
Vertex partitions of metric spaces with finite distance sets
چکیده انگلیسی

A metric space M=(M,d) is indivisible if for every colouring χ:M→2 there exists i∈2 and a copy N=(N,d) of M in M so that χ(x)=i for all x∈N. The metric space M is homogeneous if for every isometry α of a finite subspace of M to a subspace of M there exists an isometry of M onto M extending α. A homogeneous metric space UD with D as set of distances is an Urysohn metric space if every finite metric space with set of distances a subset of D has an isometry into UD. The main result of this paper states that all countable Urysohn metric spaces with a finite set of distances are indivisible.

► Which metric spaces are oscillation stable? ► A major advance in answering this question is the following theorem, which is proved in this paper: every homogeneous metric space with finite distance set is indivisible.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Discrete Mathematics - Volume 312, Issue 1, 6 January 2012, Pages 119-128
نویسندگان
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