Erdös problem on point sets - a survey
نویسنده
چکیده
This is a comprehensive survey on an interesting problem in combinatorial geometry first proposed by Erdös. The last most thorough survey in this area was by Morris and Soltan [20]. There has been a significant development in this area after this. In this survey, we present problems regarding point sets with (i) convex empty polygons and (ii) point subsets having a specified number of interior points.
منابع مشابه
Interval fractional integrodifferential equations without singular kernel by fixed point in partially ordered sets
This work is devoted to the study of global solution for initial value problem of interval fractional integrodifferential equations involving Caputo-Fabrizio fractional derivative without singular kernel admitting only the existence of a lower solution or an upper solution. Our method is based on fixed point in partially ordered sets. In this study, we guaranty the existence of special kind of ...
متن کاملA Lower Bound for an Erdös-Szekeres-Type Problem with Interior Points
A point of a finite planar point set is called an interior point of the set if it is not on the boundary of the convex hull of the set. For any positive integer n, let g(n) be the smallest integer such that every planar point set P with no three collinear points and with at least g(n) interior points has a subset Q whose the interior of the convex hull of Q contains exactly n points of P. In th...
متن کاملDirichlet Sets and Erdös-kunen-mauldin Theorem
By a theorem proved by Erdös, Kunen and Mauldin, for any nonempty perfect set P on the real line there exists a perfect set M of Lebesgue measure zero such that P +M = R. We prove a stronger version of this theorem in which the obtained perfect set M is a Dirichlet set. Using this result we show that the ideal of additive sets for any family generated by analytic subgroups of the reals contains...
متن کاملInverse Problem for Interior Spectral Data of the Dirac Operator with Discontinuous Conditions
In this paper, we study the inverse problem for Dirac differential operators with discontinuity conditions in a compact interval. It is shown that the potential functions can be uniquely determined by the value of the potential on some interval and parts of two sets of eigenvalues. Also, it is shown that the potential function can be uniquely determined by a part of a set of values of eigenfun...
متن کاملOn Best Proximity Points in metric and Banach spaces
Notice that best proximity point results have been studied to find necessaryconditions such that the minimization problemminx∈A∪Bd(x,Tx)has at least one solution, where T is a cyclic mapping defined on A∪B.A point p ∈ A∪B is a best proximity point for T if and only if thatis a solution of the minimization problem (2.1). Let (A,B) be a nonemptypair in a normed...
متن کامل