Theorems · Theorem · general topology
IsClosed.inter
∀ {X : Type u} {s₁ s₂ : Set X} [inst : TopologicalSpace X], IsClosed s₁ → IsClosed s₂ → IsClosed (s₁ ∩ s₂)- Defined in
- Mathlib.Topology.Basic
- Cited by
- 61 results in Mathlib
- Foundations
- Depth 62 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.
Cites7
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
- IsOpenproof · cited by 2,400
- IsClosedstatement and proof · cited by 1,639
- isOpen_compl_iffproof · cited by 63
- Set.compl_interproof · cited by 26
- IsOpen.unionproof · cited by 19
Cited by61
Results whose statement or proof uses this declaration.
- isClosed_Iccproof · cited by 17
- ContinuousOn.preimage_isClosed_of_isClosedproof · cited by 7
- IsClosed.sdiffproof · cited by 7
- IsLocallyClosed.interproof · cited by 6
- MeasureTheory.Measure.WeaklyRegular.innerRegular_measurableproof · cited by 4
- Homeomorph.isClosed_setOfPred_iffproof · cited by 3
- Topology.RelCWComplex.closedproof · cited by 3
- Topology.IsCoinducing.isConnected_preimage_of_isClosedproof · cited by 3
- exists_closed_nhds_one_inv_eq_mul_subsetproof · cited by 3
- exists_closed_nhds_zero_neg_eq_add_subsetproof · cited by 3
- IsClopen.interproof · cited by 3
- isClopen_inter_of_disjoint_cover_clopenproof · cited by 3