Packing dimension and Cartesian products
نویسندگان
چکیده
منابع مشابه
Packing Dimension, Hausdorff Dimension and Cartesian Product Sets
We show that the dimension adim introduced by R. Kaufman (1987) coincides with the packing dimension Dim, but the dimension aDim introduced by Hu and Taylor (1994) is different from the Hausdorff dimension. These results answer questions raised by Hu and Taylor. AMS Classification numbers: Primary 28A78, 28A80.
متن کاملPacking Measures and Dimensions on Cartesian Products
Packing measures Pg(E) and Hewitt-Stromberg measures νg(E) and their relatives are investigated. It is shown, for instance, that for any metric spaces X, Y and any Hausdorff functions f , g ν(X) ·P(Y ) 6 P(X × Y ). The inequality for the corresponding dimensions is established and used for a solution of a problem of Hu and Taylor: If X ⊆ Rn, then inf{dimPX × Y − dimPY : Y ⊆ R} = lim inf Xn↗X di...
متن کاملPacking and Domination Invariants on Cartesian Products and Direct Products
The dual notions of domination and packing in finite simple graphs were first extensively explored by Meir and Moon in [15]. Most of the lower bounds for the domination number of a nontrivial Cartesian product involve the 2-packing, or closed neighborhood packing, number of the factors. In addition, the domination number of any graph is at least as large as its 2-packing number, and the invaria...
متن کاملCombinatorial dimension in fractional Cartesian products
The combinatorial dimension relative to an arbitrary fractional Cartesian product is defined. Relations between dimensions in certain archetypal instances are derived. Random sets with arbitrarily prescribed dimensions are produced; in particular, scales of combinatorial dimension are shown to be continuously and independently calibrated. A combinatorial concept of cylindricity is key. © 2004 W...
متن کاملThe Metric Dimension of Circulant Graphs and Their Cartesian Products
Let G = (V,E) be a connected graph (or hypergraph) and let d(x, y) denote the distance between vertices x, y ∈ V (G). A subset W ⊆ V (G) is called a resolving set for G if for every pair of distinct vertices x, y ∈ V (G), there is w ∈ W such that d(x,w) 6= d(y, w). The minimum cardinality of a resolving set for G is called the metric dimension of G, denoted by β(G). The circulant graph Cn(1, 2,...
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: Transactions of the American Mathematical Society
سال: 1996
ISSN: 0002-9947,1088-6850
DOI: 10.1090/s0002-9947-96-01750-3