Metric spaces which cannot be isometrically embedded in Hilbert space
نویسندگان
چکیده
منابع مشابه
A Menger Redux: Embedding Metric Spaces Isometrically in Euclidean Space
We present geometric proofs of Menger’s results on isometrically embedding metric spaces in Euclidean space. In 1928, Karl Menger [6] published the proof of a beautiful characterization of those metric spaces that are isometrically embeddable in the ndimensional Euclidean space E. While a visitor at Harvard University and the Rice Institute in Houston during the 1930-31 academic year, Menger ga...
متن کاملMetric Spaces in Which Minimal Circuits Cannot Self-intersect
Definitions are given for self-intersecting polygons and cogeodesic points in terms of betweenness, and then it is proved that the metric spaces in which minimal polygons on a finite number of distinct noncoigeodesic points are not self-intersecting are completely characterized as those metric spaces which have the following betweenness property for any four distinct points: if b is between a a...
متن کاملOn Embedding of Finite Metric Spaces into Hilbert Space
Metric embedding plays an important role in a vast range of application areas such as computer vision, computational biology, machine learning, networking, statistics, and mathematical psychology, to name a few. The main criteria for the quality of an embedding is its average distortion over all pairs. A celebrated theorem of Bourgain states that every finite metric space on n points embeds in ...
متن کاملIsometrically Embedded Graphs
Can an arbitrary graph be embedded in Euclidean space so that the isometry group of its vertex set is precisely its graph automorphism group? This paper gives an affirmative answer, explores the number of dimensions necessary, and classifies the outerplanar graphs that have such an embedding in the plane.
متن کاملDetecting Hilbert Manifolds among Homogeneous Metric Spaces
We detect Hilbert manifolds among homogeneous metric spaces and apply the obtained results to recognizing Hilbert manifolds among homogeneous spaces of the form G/H where G is a metrizable topological group and H is a closed balanced subgroup of G.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Bulletin of the Australian Mathematical Society
سال: 1984
ISSN: 0004-9727,1755-1633
DOI: 10.1017/s0004972700001866