Abstract:An injective space is a topological space with a strong extension property for continuous maps with values on it. A certain filter space construc tion embeds every To topological space into an inject...An injective space is a topological space with a strong extension property for continuous maps with values on it. A certain filter space construc tion embeds every To topological space into an injective space. The construction gives rise to a monad. We show that the monad is of the Kock Zoberlein type and apply this to obtain a simple proof of the fact that the algebras are the con tinuous lattices (Alan Day, 1975, Oswald Wyler, 1976). In previous work we established an in jectivity theorem for monads of this type, which characterizes the injective objects over a certain class of embeddings as the algebras. For the fil ter monad, the class turns out to consist pre cisely of the subspace embeddings. We thus ob tain as a corollary tl1at the injective spaces over subspace embeddings are the continuous lattices endowed with the Scott topology (Dana Scott, 1972). Similar results are obtained for contin uous Scott domains, which are characterized as the injective spaces over dense subspace embed dings.Read More
Publication Year: 1997
Publication Date: 1997-01-01
Language: en
Type: article
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Cited By Count: 29
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