Theorems · Theorem · general topology
isClosed_preimage_val_coborder
∀ {X : Type u_1} [inst : TopologicalSpace X] {s : Set X}, IsClosed (Subtype.val ⁻¹' s)- Defined in
- Mathlib.Topology.LocallyClosed
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 73 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.
Cites12
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
- Set.Elemstatement · cited by 7,166
- Set.preimagestatement · cited by 4,946
- le_reflproof · cited by 2,061
- IsClosedstatement · cited by 1,639
- closureproof · cited by 1,254
- Set.inter_eq_rightproof · cited by 41
- coborderstatement and proof · cited by 22
- subset_coborderproof · cited by 3
- coborder_inter_closureproof · cited by 2
- isClosed_preimage_valproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- isLocallyClosed_tfaeproof · cited by 2