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Theorems · Theorem · Lie groups

neg_closure

∀ {G : Type w} [inst : TopologicalSpace G] [inst_1 : InvolutiveNeg G] [ContinuousNeg G] (s : Set G),
  -closure s = closure (-s)
Defined in
Mathlib.Topology.Algebra.Group.Basic
Cited by
2 results in Mathlib
Foundations
Depth 76 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
TopologicalSpaceInvolutiveNegContinuousNeg
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Around this declaration

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

IsOpen.closure_add · cited by 1IsOpen.closure_addIsOpen.sub_closure · cited by 0IsOpen.sub_closureSet · cited by 53352SetTopologicalSpace · cited by 24529TopologicalSpaceclosure · cited by 1254closureSet.neg · cited by 168Set.negInvolutiveNeg · cited by 151InvolutiveNegContinuousNeg · cited by 119ContinuousNegHomeomorph.neg · cited by 24Homeomorph.negHomeomorph.preimage_closure · cited by 9Homeomorph.preimage_closu…neg_closureCITED BYCITES

Cites8

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by2

Results whose statement or proof uses this declaration.