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Mathlib/Analysis/Normed/Operator Expand file tree Collapse file tree Original file line number Diff line number Diff line change @@ -68,17 +68,6 @@ theorem isCompactOperator_zero {M₁ M₂ : Type*} [Zero M₁] [TopologicalSpace
6868 [TopologicalSpace M₂] [Zero M₂] : IsCompactOperator (0 : M₁ → M₂) :=
6969 ⟨{0 }, isCompact_singleton, mem_of_superset univ_mem fun _ _ => rfl⟩
7070
71- /--
72- The identity of a topological additive group is a compact operator implies it is weakly
73- locally compact.
74- -/
75- lemma WeaklyLocallyCompactSpace.of_isCompactOperator_id
76- {M₁ : Type *} [TopologicalSpace M₁] [AddCommGroup M₁] [ContinuousAdd M₁]
77- (h : IsCompactOperator (id : M₁ → M₁)) : WeaklyLocallyCompactSpace M₁ where
78- exists_compact_mem_nhds x := by
79- obtain ⟨V, hV, hVK⟩ := h
80- exact ⟨x +ᵥ V, hV.vadd _, vadd_mem_nhds_self.2 hVK⟩
81-
8271section Characterizations
8372
8473section
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