Theorems · Theorem · general topology
Filter.coclosedCompact_eq_cocompact
∀ {X : Type u_1} [inst : TopologicalSpace X] [R1Space X], Filter.coclosedCompact X = Filter.cocompact XIn an R₁ space, the filters coclosedCompact and cocompact are equal.
- Defined in
- Mathlib.Topology.Separation.Basic
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 87 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- TopologicalSpaceR1Space
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- Filterstatement · cited by 8,121
- le_antisymmproof · cited by 2,068
- IsCompactproof · cited by 1,282
- closureproof · cited by 1,254
- subset_closureproof · cited by 309
- isClosed_closureproof · cited by 195
- Filter.cocompactstatement · cited by 141
- R1Spacestatement and proof · cited by 125
- Set.compl_subset_complproof · cited by 50
- Filter.HasBasis.le_basis_iffproof · cited by 28
Cited by5
Results whose statement or proof uses this declaration.
- HasCompactSupport.integral_Iic_deriv_eqproof · cited by 1
- Rat.not_countably_generated_nhds_infty_opcproof · cited by 1
- OnePoint.continuous_iff_from_discreteproof · cited by 1
- HasCompactSupport.integral_Ioi_deriv_eqproof · cited by 0
- Bornology.relativelyCompact_eq_inCompactproof · cited by 0