Theorems · Theorem · general topology
countable_setOfPred_covBy_right
∀ {α : Type u} [inst : TopologicalSpace α] [inst_1 : LinearOrder α] [OrderTopology α] [SecondCountableTopology α],
{x | ∃ y, x ⋖ y}.CountableThe set of points which are isolated on the right is countable when the space is second-countable.
- Defined in
- Mathlib.Topology.Order.Basic
- Cited by
- 3 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.
Cites45
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
- LinearOrderstatement and proof · cited by 8,572
- Set.ofPredstatement and proof · cited by 6,101
- LE.le.transproof · cited by 3,151
- Set.iUnionproof · cited by 2,483
- Nontrivialproof · cited by 2,416
- IsOpenproof · cited by 2,400
- le_rflproof · cited by 1,558
- OrderTopologystatement and proof · cited by 1,355
- Set.Iooproof · cited by 1,214
- Set.Iocproof · cited by 971
Cited by3
Results whose statement or proof uses this declaration.
- Set.PairwiseDisjoint.countable_of_Iooproof · cited by 4
- countable_setOfPred_isolated_rightproof · cited by 2
- countable_setOf_covBy_rightproof · cited by 0