Timeline for Compact-open Topology for Partial Maps?

6 events

when toggle format	what		by	license	comment
Dec 9, 2023 at 22:23	answer	added	Joseph Van Name		timeline score: 2
Dec 9, 2023 at 1:00	comment	added	Emily		This should lead to a bunch of different notions and potential definitions/topologies, but I'm not sure how useful this point of view might be
Dec 9, 2023 at 0:58	comment	added	Emily		For example, the definitions of lower semicontinuous and upper semicontinuous relations here would lead to two other notions of continuity, which may or may not agree with the definition you gave (I haven't checked). We could also view relations as maps $\mathcal{P}(X)\to Y$, and use one of the topologies on $\mathrm{Hom}(\mathcal{P}(X),Y)$, choosing one for $\mathcal{P}(X)$ too (there are many choices) if needed. Then we use the subspace topology on the subspace of $\mathrm{Hom}(\mathcal{P}(X),Y)$ spanned by the partial maps/functional relations
Dec 9, 2023 at 0:57	comment	added	Emily		Another possibility, not sure how useful, would be to view partial maps as functional relations, those relations $R\colon X\to Y$ such that $R(a)$ has at most one element for each $a\in A$. Then we could apply some of the stuff that has been developed for relations between topological spaces, their continuity, and the spaces of maps between them.
Dec 8, 2023 at 16:37	history	edited	Bumblebee	CC BY-SA 4.0	edited tags
Dec 8, 2023 at 16:28	history	asked	Bumblebee	CC BY-SA 4.0