Separation properties of polygons in R ²

Abstract

We recall that a set N is a neighborhood of a set M if N contains an open set which contains M. The standard n-ball is

$${B^n} = \left\{ {P|P \in {R^n} and\,d\left( {{P_0},P} \right) \leqslant \,1} \right\},$$

where P ₀ is the origin in R ⁿ. The standard n-sphere is

$${S^n} = \left\{ {P|P \in {R^n} and\,d\left( {{P_0},P} \right) = \,1} \right\}.$$