Properly injective spaces and function spaces

@inproceedings{Escard2001ProperlyIS,
  title={Properly injective spaces and function spaces},
  author={Mart́ın H{\"o}tzel Escard{\'o}},
  year={2001}
}
  • 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

Citations

Publications citing this paper.
Showing 1-10 of 31 extracted citations

References

Publications referenced by this paper.
Showing 1-8 of 8 references

Domain theory

  • D. M. Gabbay
  • 1994

Stably continuous frames , and their topological manifestations

  • K. H. Hofmann.
  • 1992

Another look at the localic Tychonoff Theorem

  • B. A. Davey, A. H.
  • Commentationes Mathematice Universitatis…

Similar Papers

Loading similar papers…