A space $X$ whose topology agrees with the final topology with respect to all maps $I\to X$ is often called a delta-generated ($\Delta$-generated) space. The category of $\Delta$-generated spaces is a convenient category of spaces (in the sense of Steenrod) and is used in Diffeology, String Topology, and generalized covering spaces theories.

A space $X$ whose topology agrees with the final topology with respect to all maps $I\to X$ is often called a delta-generated ($\Delta$-generated) space. The category of $\Delta$-generated spaces is a convenient category of spaces (in the sense of Steenrod) and is used in Diffeology, directed homotopy, and generalized covering spaces theories.