منابع مشابه
Sets, complements and boundaries
The relations among a set, its complement, and its boundary are examined constructively. A crucial tool is a theorem that allows the construction of a point where a segment comes close to the boundary of a set in a Banach space. Brouwerian examples show that many of the results are the best possible.
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متن کاملDisjoint representability of sets and their complements
For a hypergraph H and a set S, the trace of H on S is the set of all intersections of edges of H with S. We will consider forbidden trace problems, in which we want to find the largest hypergraph H that does not contain some list of forbidden configurations as traces, possibly with some restriction on the number of vertices or the size of the edges in H. In this paper we will focus on combinat...
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 کاملComplements of Subanalytic Sets and Existential Formulas for Analytic Functions
We show that the complement of a subanalytic set defined by real analytic functions from any subalgebra closed under differentiation is a subanalytic set defined by the functions from the same subalgebra. This result has an equivalent formulation in logic: Consider an expression built from functions as above using equalities and inequalities as well as existential and universal quantifiers. Suc...
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ژورنال
عنوان ژورنال: Indagationes Mathematicae
سال: 1996
ISSN: 0019-3577
DOI: 10.1016/s0019-3577(97)89131-8