locallyFinite_tsupport — Mathlib

English

The family of topological supports tsupport(f_i) is locally finite: for each x, only finitely many i satisfy x ∈ tsupport(f_i).

Русский

Семейство топологических опор tsupport(f_i) локально конечно: для каждого x существует конечное множество индексов i с x ∈ tsupport(f_i).

LaTeX

$$$\text{LocallyFinite }(i \mapsto tsupport(f_i))$; equivalently, for every $x \in X$, the set $\{i \mid x \in tsupport(f_i)\}$ is finite.$$

Lean4

theorem locallyFinite_tsupport : LocallyFinite fun i => tsupport (f i) :=
  f.locallyFinite.closure

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