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- W57183862 abstract "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 → Set to the category of sets and relations. (U , η, μ) fails to be a monad on Rel only because η is not a strict natural transformation. So, exponentiable spaces are the lax (with respect to the unit law) algebras for a lax monad on Rel . Strict algebras are exponentiable and T1 spaces." @default.
- W57183862 created "2016-06-24" @default.
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- W57183862 date "2001-01-01" @default.
- W57183862 modified "2023-09-27" @default.
- W57183862 title "CONVERGENCE IN EXPONENTIABLE SPACES" @default.
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