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feat: "outer product" of functions that tend to zero on the cocompact filter

Open trivial1711 opened this issue 10 months ago • 3 comments

Let M be a topological space with a continuous multiplication operation and a zero.

We prove that if f : α → M and g : β → M are continuous functions that both tend to zero on the cocompact filter, then the "outer product" fun (i : α × β) ↦ (f i.1) * (g i.2) also tends to zero on the cocompact filter.

We then specialize this result to the case that α and β have the discrete topology.


  • [x] depends on: #12305 Open in Gitpod

trivial1711 avatar Apr 21 '24 10:04 trivial1711