Neighbourhood retract

Definition with symbols
A subspace $$A$$ of a topological space $$X$$ is termed a neighbourhood retract in $$X$$ is there is an open subset $$U$$ of $$X$$ containing $$A$$, such that $$A$$ is a retract of $$U$$.

Stronger properties

 * Strong deformation retract
 * Homotopy retract
 * Retract
 * Open subset

Metaproperties
If $$A$$ is a neighbourhood retract of $$B$$ and $$B$$ is a neighbourhood retract of $$C$$, then we can find a neighbourhood of $$A$$ in $$C$$, for which it is a retract.