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 $g:T \to S$: $g \restriction H = f$

Sources

• 1980: G. Gierz, K.H. Hofmann, K. Keimel, J.D. Lawson, M.W. Mislove and D.S. Scott: A Compendium of Continuous Lattices

• Mizar article WAYBEL18:def 5