Embeddings of finite-dimensional spaces into finite products of 1-dimensional spaces
نویسندگان
چکیده
منابع مشابه
Isometric Embeddings of Snowflakes into Finite-dimensional Banach Spaces
We consider a general notion of snowflake of a metric space by composing the distance with a nontrivial concave function. We prove that a snowflake of a metric space X isometrically embeds into some finite-dimensional normed space if and only if X is finite. In the case of power functions we give a uniform bound on the cardinality of X depending only on the power exponent and the dimension of t...
متن کاملFinite Dimensional Generating Spaces of Quasi-Norm Family
In this paper,~some results on finite dimensional generating spaces of quasi-norm family are established.~The idea of equivalent quasi-norm families is introduced.~Riesz lemma is established in this space.~Finally,~we re-define B-S fuzzy norm and prove that it induces a generating space of quasi-norm family.
متن کاملRegularity of embeddings of infinite-dimensional fractal sets into finite-dimensional spaces
We consider the image of a fractal set X in a Banach space under typical linear and nonlinear projections π intoR . We prove that whenN exceeds twice the box-counting dimension of X, then almost every (in the sense of prevalence) such π is one-to-one on X, and we give an explicit bound on the Hölder exponent of the inverse of the restriction of π toX. The same quantity also bounds the factor by...
متن کاملQuantum approximation I. Embeddings of finite-dimensional Lp spaces
We study approximation of embeddings between finite dimensional Lp spaces in the quantum model of computation. For the quantum query complexity of this problem matching (up to logarithmic factors) upper and lower bounds are obtained. The results show that for certain regions of the parameter domain quantum computation can essentially improve the rate of convergence of classical deterministic or...
متن کاملEmbeddings of Locally Finite Metric Spaces into Banach Spaces
We show that if X is a Banach space without cotype, then every locally finite metric space embeds metrically into X.
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: Topology and its Applications
سال: 1991
ISSN: 0166-8641
DOI: 10.1016/0166-8641(91)90061-p