We prove the topological invariance of the combinatorial Euler characteristic of ominimal sets with the help of a canonical, topologically defined stratification of o-minimal sets by locally compact ones. Introduction. Let Bn be the collection of semi-algebraic subsets of R, i.e. sets definable by a finite boolean combination of polynomial equalities and inequalities. The Bn, n ∈ N, satisfy (i)...

We prove the existence of free boundary minimal annuli inside suitably convex subsets of three-dimensional Riemannian manifolds with nonnegative Ricci curvature − including strictly convex domains of the Euclidean space R.

This paper presents the results of a study on the use of morphological set operations to represent and encode a discrete binary image by parts of its skeleton, a thinned version of the image containing complete information about its shape and size. Using morphological erosions and openings, a finite image can be uniquely decomposed into a finite number of skeleton subsets and then the image can...

OF THE DISSERTATION On Generation of Cut Conjunctions, Minimal k-Connected Spanning Subgraphs, Minimal Connected and Spanning Subsets and Vertices by Konrad Borys Dissertation Director: Professor Endre Boros We consider the following problems: • Cut conjunctions in graphs: given an undirected graphG = (V,E) and a collection of vertex pairs B ⊆ V × V generate all minimal edge sets X ⊆ E such tha...

This article is a fundamental study in computable analysis. In the framework of Type-2 effectivity, TTE, we investigate computability aspects on finite and infinite products of effective topological spaces. For obtaining uniform results we introduce natural multi-representations of the class of all effective topological spaces, of their points, of their subsets and of their compact subsets. We ...

We show that the minimal cardinality of a dense subset of the measure algebra is the same as the minimal cardinality of a base of the ideal of Lebesgue measure zero subsets of the real line. 0. Introduction. Let (F, <) be a given partial ordering. A subset D ç P is called dense if for any p g F there exists d g D such that d < p. A subset D is called upward dense if D is dense in (F, > ). Let A...

We study the problem of adding edges to a given arbitrary graph so that the resulting graph is a split graph, called a split completion of the input graph. Our purpose is to add an inclusion minimal set of edges to obtain a minimal split completion, which means that no proper subset of the added edges is sufficient to create a split completion. Minimal completions of arbitrary graphs into chord...

Let C be a finite set of n elements and R = {r1, r2, . . . , rm} a family of m subsets of C. A subset X of R verifies the Consecutive Ones Property (C1P) if there exists a permutation P of C such that each ri in X is an interval of P . A Minimal Conflicting Set (MCS) S ⊆ R is a subset of R that does not verify the C1P, but such that any of its proper subsets does. In this paper, we present a ne...

In [Berarducci-Otero, 2004], the authors define an analogue of Lebesgue measure for bounded definable subsets of an o-minimal structure K , which expands a real closed field. Our aim is defining the area of a bounded definable d-dimensional subsets of Kn. Different possible definitions for such area are possible: we will prove that some of them are equivalent. On the reals, there are many diffe...