final topology

Short definition from Wiktionary

Noun

1. 1
   Given a set X, a family of topological spaces (M#95;i,T#95;i)#95;#123;i#92;inI#125; and a family of functions f#95;i#58;M#95;i#92;toX, the final topology is the finest topology on X such that all f#95;i are continuous.