Certain inequalities concerning bicentric quadrilaterals, hexagons and octagons.
Coincidences of simplex centers and related facial structures.
Concerning the order and the semi-order of n-dimensional Euclidean space
Countably convex sets
We investigate countably convex subsets of Banach spaces. A subset of a linear space is countably convex if it can be represented as a countable union of convex sets. A known sufficient condition for countable convexity of an arbitrary subset of a separable normed space is that it does not contain a semi-clique [9]. A semi-clique in a set S is a subset P ⊆ S so that for every x ∈ P and open neighborhood u of x there exists a finite set X ⊆ P ∩ u such that conv(X) ⊈ S. For closed sets this condition...
Covering the plane with sprays
For any three noncollinear points c₀,c₁,c₂ ∈ ℝ², there are sprays S₀,S₁,S₂ centered at c₀,c₁,c₂ that cover ℝ². This improves the result of de la Vega in which c₀,c₁,c₂ were required to be the vertices of an equilateral triangle.