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Theorems · Theorem · Lie groups

ContinuousAt.inv

∀ {G : Type u_1} {X : Type u_3} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace G] [inst_2 : Inv G]
  [ContinuousInv G] {f : X → G} {x : X}, ContinuousAt f x → ContinuousAt f⁻¹ x
Defined in
Mathlib.Topology.Algebra.Group.Defs
Cited by
2 results in Mathlib
Foundations
Depth 60 from the axioms · uses propext, Quot.sound
Assumes
TopologicalSpaceTopologicalSpaceInvContinuousInv
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

exists_nhds_split_inv · cited by 1exists_nhds_split_invContinuousAt.fun_inv · cited by 0ContinuousAt.fun_invTopologicalSpace · cited by 24529TopologicalSpaceContinuousAt · cited by 697ContinuousAtContinuousInv · cited by 89ContinuousInvFilter.Tendsto.inv · cited by 7Tendsto.invContinuousAt.invCITED BYCITES

Cites4

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Cited by2

Results whose statement or proof uses this declaration.