Definition:Injective Space
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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