Strong and Weak n-Homogeneous Spaces

Abstract

In this paper we introduce new types of n-homogeneity, we call them n-homogeneous of type 2 and type 3, denoted by nH2, nH3 respectively. We show that every 3H3-space is bihomogeneous space. Also, every finite nH3-space has the trivial topology (discrete or indiscrete). We show that every 3H3-space is strong 2-homogeneous. We study the implications between these spaces with the well known spaces, strongly n-homogeneous spaces and weakly n-homogeneous spaces.