Theorems · Theorem · general topology
cocompact_eq_atBot_atTop
∀ {α : Type u_2} [inst : LinearOrder α] [inst_1 : TopologicalSpace α] [NoMaxOrder α] [NoMinOrder α]
[OrderClosedTopology α] [CompactIccSpace α], Filter.cocompact α = Filter.atBot ⊔ Filter.atTop- Defined in
- Mathlib.Topology.Order.Compact
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 90 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- TopologicalSpacestatement and proof · cited by 24,529
- LinearOrderstatement and proof · cited by 8,572
- Filterstatement · cited by 8,121
- Filter.atTopstatement · cited by 2,405
- Filter.atBotstatement · cited by 512
- LE.le.antisymmproof · cited by 507
- OrderClosedTopologystatement and proof · cited by 445
- NoMaxOrderstatement and proof · cited by 340
- NoMinOrderstatement and proof · cited by 247
- Filter.cocompactstatement · cited by 141
- CompactIccSpacestatement and proof · cited by 96
- cocompact_le_atBot_atTopproof · cited by 2
Cited by6
Results whose statement or proof uses this declaration.
- Int.cofinite_eqproof · cited by 7
- PhragmenLindelof.right_half_plane_of_tendsto_zero_on_realproof · cited by 2
- cexp_neg_quadratic_isLittleO_abs_rpow_cocompactproof · cited by 2
- Continuous.isBounded_range_iff_isBigO_atTop_atBotproof · cited by 1
- isBigO_norm_restrict_cocompactproof · cited by 1
- tendsto_rpow_abs_mul_exp_neg_mul_sq_cocompactproof · cited by 0