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Theorems · Theorem · general topology

isClosedMap_smul

∀ {α : Type u_2} {G : Type u_4} [inst : TopologicalSpace α] [inst_1 : Group G] [inst_2 : MulAction G α]
  [ContinuousConstSMul G α] (c : G), IsClosedMap fun x => c • x
Defined in
Mathlib.Topology.Algebra.ConstMulAction
Cited by
2 results in Mathlib
Foundations
Depth 77 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
TopologicalSpaceGroupMulActionContinuousConstSMul
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Around this declaration

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

IsClosed.smul · cited by 5IsClosed.smulIsUnit.isClosedMap_smul · cited by 0IsUnit.isClosedMap_smulTopologicalSpace · cited by 24529TopologicalSpaceGroup · cited by 6238GroupMulAction · cited by 1294MulActionContinuousConstSMul · cited by 832ContinuousConstSMulIsClosedMap · cited by 138IsClosedMapHomeomorph.smul · cited by 21Homeomorph.smulHomeomorph.isClosedMap · cited by 18Homeomorph.isClosedMapisClosedMap_smulCITED BYCITES

Cites7

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.