Theorems · Theorem · general topology
isLocallyClosed_iff_isOpen_coborder
∀ {X : Type u_1} [inst : TopologicalSpace X] {s : Set X}, IsLocallyClosed s ↔ IsOpen (coborder s)- Defined in
- Mathlib.Topology.LocallyClosed
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 75 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- TopologicalSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- nhdsproof · cited by 5,554
- Set.preimageproof · cited by 4,946
- IsOpenstatement and proof · cited by 2,400
- IsClosedproof · cited by 1,639
- closureproof · cited by 1,254
- List.TFAE.outproof · cited by 177
- IsLocallyClosedstatement and proof · cited by 44
- coborderstatement and proof · cited by 22
- isLocallyClosed_tfaeproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- IsLocallyClosed.isOpen_coborderproof · cited by 1