Convergence in Exponentiable Spaces

@inproceedings{Pisani2001ConvergenceIE,
  title={Convergence in Exponentiable Spaces},
  author={Claudio Pisani},
  year={2001}
}
Exponentiable spaces are characterized in terms of convergence. More precisely, we prove that a relation R : UX ⇀ X between ultrafilters and elements of a set X is the convergence relation for a quasi-locally-compact (that is, exponentiable) topology on X if and only if the following conditions are satisfied: 1. id ⊆ R ◦ η 2. R ◦ UR = R ◦ μ where η : X → UX and μ : U(UX) → UX are the unit and the multiplication of the ultrafilter monad, and U : Rel → Rel extends the ultrafilter functor U : Set… CONTINUE READING

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