Retract
This article defines a property over pairs of a topological space and a subspace, or equivalently, properties over subspace embeddings (viz, subsets) in topological spaces
Definition
A subspace of a topological space is said to be a retract if there is a continuous map on the whole topological space that maps everything to within the subspace, and that is identity on the retract. In other words, there is a continuous idempotent map whose image-cum-fixed-point space is precisely the given subspace. Such a map is termed a retraction.
Facts
Clearly the whole space is a retract of itself (the identity map being a retraction) and every one-point subspace is also a retract (the constant map to that one point being the retraction).