منابع مشابه
The Transfinite Hausdorff Dimension
Making an extensive use of small transfinite topological dimension trind, we ascribe to every metric space X an ordinal number (or −1 or Ω) tHD(X), and we call it the transfinite Hausdorff dimension of X. This ordinal number shares many common features with Hausdorff dimension. It is monotone with respect to subspaces, it is invariant under bi-Lipschitz maps (but in general not under homeomorph...
متن کاملA lower bound on dimension reduction for trees in \ell_1
There is a constant c > 0 such that for every ε ∈ (0, 1) and n > 1/ε, the following holds. Any mapping from the n-point star metric into l1 with bi-Lipschitz distortion 1 + ε requires dimension d > c log n ε log(1/ε) .
متن کاملA Homological Lower Bound for Order Dimension of Lattices
We prove that if a nite lattice L has order dimension at most d, then the homology of the order complex of its proper part L vanishes in dimensions d ? 1 and higher. In case L can be embedded as a join-sublattice in N d then L actually has the homotopy type of a simplicial complex with d vertices. 1. Introduction. The order dimension OrderDim(P) of a nite partially ordered set (poset for short)...
متن کاملA Lower Bound for Families of Natarajan Dimension d
A system F of functions f1; 2 most d if no (d + 1)-element subset A X is 2-shattered. A is 2-shattered if for each x 2 A there is a 2-element set V x f1; 2; : : :; kg such that for any choice of elements c x 2 V x , a function f 2 F exists with f(x) = c x for all x 2 A. We improve a lower bound of c d k d n d (due to Haussler and Long) for the maximum size of F of Natarajan dimension at most d ...
متن کاملA Lower Bound for Weak epsilon-Nets in High Dimension
A nite set N R d is a weak "-net for an n-point set X R d (with respect to convex sets) if it intersects each convex set K with jK \ Xj "n. It is shown that there are point sets X R d for which every weak 1 50-net has at least const e p d=2 points. Weak "-nets with respect to convex sets, as deened in the abstract, were introduced by Haussler and Welzl 6] and later applied in results in discret...
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: Fundamenta Mathematicae
سال: 1968
ISSN: 0016-2736,1730-6329
DOI: 10.4064/fm-63-2-167-173