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