Theorems · Theorem · general topology
interior_Icc
∀ {α : Type u_1} [inst : TopologicalSpace α] [inst_1 : LinearOrder α] [OrderTopology α] [DenselyOrdered α]
[NoMinOrder α] [NoMaxOrder α] {a b : α}, interior (Set.Icc a b) = Set.Ioo a b- Defined in
- Mathlib.Topology.Order.DenselyOrdered
- Cited by
- 37 results in Mathlib
- Foundations
- Depth 87 from the axioms · uses propext, Classical.choice, Quot.sound
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.
- Setstatement and proof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- LinearOrderstatement and proof · cited by 8,572
- Set.Iccstatement · cited by 1,702
- Set.Ioiproof · cited by 1,463
- OrderTopologystatement and proof · cited by 1,355
- Set.Ioostatement and proof · cited by 1,214
- Set.Iicproof · cited by 1,111
- interiorstatement and proof · cited by 714
- DenselyOrderedstatement and proof · cited by 471
- NoMaxOrderstatement and proof · cited by 340
- NoMinOrderstatement and proof · cited by 247
Cited by37
Results whose statement or proof uses this declaration.
- uniqueDiffOn_Iccproof · cited by 21
- interior_closedBallproof · cited by 8
- MeasureTheory.integral_divergence_of_hasFDerivAt_off_countable_of_equivproof · cited by 2
- strictConcaveOn_sin_Iccproof · cited by 2
- exists_hasDerivWithinAt_eq_of_gt_of_ltproof · cited by 2
- Convex.nontrivial_iff_nonempty_interiorproof · cited by 2
- MeasureTheory.integrableOn_Icc_deriv_smul_iff_of_deriv_nonposproof · cited by 1
- Real.strictConcaveOn_qaryEntropyproof · cited by 1
- exists_dist_slope_lt_pairwiseDisjoint_hasSumproof · cited by 1
- Real.sum_range_le_log_divproof · cited by 1
- intervalIntegral.integral_deriv_smul_comp_of_deriv_nonnegproof · cited by 1