Theorems · Theorem · general topology
closure_ordConnected_inter_rat
∀ {s : Set ℝ}, s.OrdConnected → s.Nontrivial → closure (s ∩ Set.range Rat.cast) = closure s- Defined in
- Mathlib.Topology.Instances.Real.Lemmas
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 116 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites27
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
- Realstatement and proof · cited by 25,697
- Set.rangestatement and proof · cited by 4,705
- LT.lt.leproof · cited by 2,189
- absproof · cited by 1,814
- closurestatement · cited by 1,254
- LE.le.antisymmproof · cited by 507
- Set.inter_subset_leftproof · cited by 360
- isClosed_closureproof · cited by 195
- Set.OrdConnectedstatement and proof · cited by 161
- sub_posproof · cited by 147
- Set.Nontrivialstatement and proof · cited by 145
Cited by1
Results whose statement or proof uses this declaration.
- closure_of_rat_image_ltproof · cited by 0