# Definition:Injective Space

## Definition

Let $Z = \left({S, \tau_1}\right)$ be a topological space.

Then $Z$ is injective (space) if and only if

for all topological spaces $X = \left({H, \tau_2}\right)$
and for all continuous mappings $f:H \to S$
and for all topological spaces $Y = \left({T, \tau_3}\right)$ such that $X$ is topological subspace of $Y$:
there exists a continuous mapping $g:T \to S$: $g \restriction H = f$