On the Countable Dense Homogeneity of Euclidean Spaces

Abstract

A countable dense homogeneous space, in a general sense, is a topological space in which any two countable dense subsets of the space are "dispersed" the same way. In this thesis, we will show that some very well-known topological spaces, such as n-dimensional Euclidean space R^n and the n-sphere S^n for all natural numbers n is countable dense homogeneous.