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Theorems · Definition · general topology

TopologicalSpace.Clopens.toOpens

{α : Type u_2} → [inst : TopologicalSpace α] → TopologicalSpace.Clopens α → TopologicalSpace.Opens α

Reinterpret a clopen as an open.

Defined in
Mathlib.Topology.Sets.Closeds
Cited by
3 results in Mathlib
Foundations
Depth 11 from the axioms · uses no axioms
Assumes
TopologicalSpace
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Around this declaration

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

PrimeSpectrum.basicOpen_isIdempotentElemEquivClopens_symm · cited by 0PrimeSpectrum.basicOpen_i…PrimeSpectrum.isIdempotentElemEquivClopens_apply_toOpens · cited by 0PrimeSpectrum.isIdempoten…TopologicalSpace.Clopens.coe_toOpens · cited by 0Clopens.coe_toOpensTopologicalSpace · cited by 24529TopologicalSpaceSetLike.coe · cited by 8199SetLike.coeTopologicalSpace.Opens · cited by 2040TopologicalSpace.OpensTopologicalSpace.Clopens · cited by 53TopologicalSpace.ClopensTopologicalSpace.Clopens.isOpen · cited by 1Clopens.isOpenClopens.toOpensCITED BYCITES

Cites5

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Cited by3

Results whose statement or proof uses this declaration.