Dominant of a topological space

$X$

Any topological space for which $X$ serves as a retract (cf. Retract of a topological space).

#### Comments[edit]

This is not standard Western terminology; there is in fact no name for this concept. The standard Western usage of dominating is as follows: A space $X$ is said to dominate a space $Y$ if and only if there are continuous mappings $f : X \rightarrow Y$ and $g : Y \rightarrow X$ such that $fg$ is homotopic to the identity mapping (on $Y$).