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- W1977037756 abstract "We study generalized ordered spaces in which every closed subspace is π-embedded and which satisfy the Dugundji Extension Theorem. We prove: Let X be a perfectly normal generalized ordered space in which the set E(X) = {x ϵ X: (→,x] or [x,→) is open in X} is σ-discrete in X. Then every closed subspace of X is π-embedded. Furthermore, for every closed subspace A of X and for any locally convex linear topological space Z there is a linear transformation u : C(A,Z) → C(X,Z) such that for each f ϵ C(A,Z), u(f) is an extension of f and the range of u(f) is contained in the closed convex hull of the range of f. This is a partial answer to a question asked by Heath and Lutzer (1974)." @default.
- W1977037756 created "2016-06-24" @default.
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- W1977037756 date "1998-04-01" @default.
- W1977037756 modified "2023-10-16" @default.
- W1977037756 title "π-embeddings and Dugundji extension theorems for generalized ordered spaces" @default.
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- W1977037756 doi "https://doi.org/10.1016/s0166-8641(97)00081-3" @default.
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