Properly injective spaces and function spaces

  title={Properly injective spaces and function spaces},
  author={Mart́ın H{\"o}tzel Escard{\'o}},
  • Mart́ın Hötzel Escardó
  • Published 2001
Given an injective space D (a continuous lattice endowed with the Scott topology) and a subspace embedding j : X → Y , Dana Scott asked whether the higher-order function [X → D] → [Y → D] which takes a continuous map f : X → D to its greatest continuous extension f̄ : Y → D along j is Scott continuous. In this case the extension map is a subspace embedding. We show that the extension map is Scott continuous iff D is the trivial one-point space or j is a proper map in the sense of Hofmann and… CONTINUE READING


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