Theorems · Theorem · general topology
IsClosed.sdiff
∀ {X : Type u} {s t : Set X} [inst : TopologicalSpace X], IsClosed s → IsOpen t → IsClosed (s \ t)- Defined in
- Mathlib.Topology.Basic
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 63 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.
Cites6
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
- IsOpenstatement and proof · cited by 2,400
- IsClosedstatement and proof · cited by 1,639
- IsClosed.interproof · cited by 61
- isClosed_compl_iffproof · cited by 35
Cited by7
Results whose statement or proof uses this declaration.
- Valued.valuedCompletion_surjective_iffproof · cited by 2
- BoxIntegral.integrable_of_bounded_and_ae_continuousWithinAtproof · cited by 2
- IsClosed.everywherePosSubsetproof · cited by 2
- minimal_nonempty_closed_subsingletonproof · cited by 1
- IsCompact.binary_compact_coverproof · cited by 1
- exists_countable_union_perfect_of_isClosedproof · cited by 1