Characterization of finite-dimensional $Z$-sets
نویسندگان
چکیده
منابع مشابه
A characterization of finite sets that tile the integers
A set of integers A is said to tile the integers if there is a set C ⊂ Z such that every integer n can be written in a unique way as n = a+ c with a ∈ A and c ∈ C. Throughout this paper we will assume that A is finite. It is well known (see [7]) that any tiling of Z by a finite set A must be periodic: C = B + MZ for some finite set B ⊂ Z such that |A| |B| = M . We then write A⊕B = Z/MZ. Newman ...
متن کاملZero sets in pointfree topology and strongly $z$-ideals
In this paper a particular case of z-ideals, called strongly z-ideal, is defined by introducing zero sets in pointfree topology. We study strongly z-ideals, their relation with z-ideals and the role of spatiality in this relation. For strongly z-ideals, we analyze prime ideals using the concept of zero sets. Moreover, it is proven that the intersection of all zero sets of a prime ideal of C(L),...
متن کاملFunctional Analysis Lecture Notes: Compact Sets and Finite-dimensional Spaces
Definition 1.1 (Compact and Totally Bounded Sets). Let X be a metric space, and let E ⊆ X be given. (a) We say that E is compact if every open cover of E contains a finite subcover. That is, E is compact if whenever {Uα}α∈I is a collection of open sets whose union contains E, then there exist finitely many α1, . . . , αN such that E ⊆ Uα1 ∪ · · · ∪ UαN . (b) We say that E is sequentially compac...
متن کاملFinite Sets as Complements of Finite Unions of Convex Sets
Suppose S ⊆ R is a set of (finite) cardinality n whose complement can be written as the union of k convex sets. It is perhaps intuitively appealing that when n is large k must also be large. This is true, as is shown here. First the case in which the convex sets must also be open is considered, and in this case a family of examples yields an upper bound, while a simple application of a theorem ...
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 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: Proceedings of the American Mathematical Society
سال: 1974
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1974-0334221-8