Theorems · Theorem · general topology
closure_empty
∀ {X : Type u} [inst : TopologicalSpace X], closure ∅ = ∅- Defined in
- Mathlib.Topology.Closure
- Cited by
- 11 results in Mathlib
- Foundations
- Depth 66 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.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- closurestatement · cited by 1,254
- IsClosed.closure_eqproof · cited by 139
- isClosed_emptyproof · cited by 26
Cited by11
Results whose statement or proof uses this declaration.
- tsupport_zeroproof · cited by 2
- closure_empty_iffproof · cited by 2
- interior_extChartAt_target_nonemptyproof · cited by 1
- Set.hasSeparatingCover_empty_leftproof · cited by 1
- mulTSupport_oneproof · cited by 1
- Metric.cthickening_eq_biUnion_closedBallproof · cited by 1
- tsupport_fun_zeroproof · cited by 0
- Filter.lift'_closure_eq_botproof · cited by 0
- mulTSupport_fun_oneproof · cited by 0
- isNowhereDense_emptyproof · cited by 0