Tri Topological spaces - An Overview

Abstract

A N-topological space is a set equipped with $N$ arbitrary topologies. If $T_1, T_2, ..., T_N$ are $N$ topologies defined on a nonempty
set $X$, then the $N-$topological space is denoted by $(X, T_1, T_2, ..., T_N )$. To denote a topology we use the symbol $T$ for convenience. This article is a study on tri topological space. Some definitions related to topological space are discussed first. Subsequently, the tri topological space with example, characterisation, tri $\alpha$ continuous functions, tri $\alpha$ homeomorphisms, tri $\alpha$ biconnected spaces and discussed.