Certain topological qualities of convex sets in Euclidean space

Characterizing Certain Staircase Convex Sets in R

Let C = {C1, . . . , Cn} be a family of distinct boxes in R whose intersection graph is a tree, and let S = C1∪· · ·∪Cn. Let T ⊆ S. The set T lies in a staircase convex subset of S if and only if for every a, b in T there is an a−b staircase path in S. This result, in turn, yields necessary and sufficient conditions for S to be a union of k staircase convex sets, k ≥ 1. Analogous results charac...

Angle and Triangle in Euclidean Topological Space

Two transformations between the complex space and 2dimensional Euclidean topological space are defined. By them, the concept of argument is induced to 2-dimensional vectors using argument of complex number. Similarly, the concept of an angle is introduced using the angle of two complex numbers. The concept of a triangle and related concepts are also defined in n-dimensional Euclidean topologica...

On the Geometry of m-Convex Sets in the Euclidean space

A set A in Euclidean n-space En, is called an m-convex set if for every m distinct points of A at least one of the line segments joining two points of them lies in A. In this article we study some geometrical and topological properties of these sets in En. Mathematics Subject Classification: 53C42, 52A05

On Contiguous Congruent Sets in Euclidean Space

g*Λ Closed Sets in Topological Space

The generalized closed sets in point set topology have been found considerable interest among general topologists. In this paper, we introduce and study topological properties of g*Λ closed and open sets and its relationships with other generalized closed sets are investigated.