Commit 2023-07-16 14:44 1a646ca7

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feat(Topology.Algebra.InfiniteSum): make sure that tsum and sum coincide on fintypes (#5914) Currently, when s is a fintype, it is possible that ∑' x, f x ≠ ∑ x, f x (if the topology of the target space is not separated), as the infinite sum ∑' picks some limit if it exists, but not necessarily the one we prefer. This PR tweaks the definition of infinite sums to make sure that, when a function is finitely supported, the chosen limit for its infinite sum is the (finite) sum of its values. This makes it possible to remove a few separation assumption here and there.

Estimated changes

modified theorem tsum_congr
modified theorem tsum_empty
added theorem tsum_eq_finsum
modified theorem tsum_eq_sum
modified theorem tsum_fintype
modified theorem tsum_pi_single
deleted theorem tsum_zero'
modified theorem tsum_zero