Theorems · Definition · global analysis
IccLeftChart
(x y : ℝ) → [h : Fact (x < y)] → OpenPartialHomeomorph (↑(Set.Icc x y)) (EuclideanHalfSpace 1)
The left chart for the topological space [x, y], defined on [x,y) and sending x to 0 in
EuclideanHalfSpace 1.
- Defined in
- Mathlib.Geometry.Manifold.Instances.Real
- Cited by
- 14 results in Mathlib
- Foundations
- Depth 167 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Fact
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Realstatement and proof · cited by 25,697
- Set.Elemstatement and proof · cited by 7,166
- Set.ofPredproof · cited by 6,101
- Factstatement and proof · cited by 2,726
- Set.Iccstatement and proof · cited by 1,702
- OpenPartialHomeomorphstatement · cited by 664
- WithLp.ofLpproof · cited by 323
- EuclideanHalfSpacestatement and proof · cited by 47
Cited by14
Results whose statement or proof uses this declaration.
- contMDiffOn_projIccproof · cited by 4
- isImmersionOfComplement_subtypeVal_Iccproof · cited by 3
- Icc_chartedSpaceChartAt_of_le_topstatement and proof · cited by 2
- IccLeftChart_extend_botstatement · cited by 1
- IccLeftChart_extend_bot_mem_frontierstatement · cited by 1
- IccLeftChart_extend_interior_posstatement · cited by 1
- IccLeftChart_symm_apply_of_lestatement · cited by 1
- Icc_chartedSpaceChartAt_of_top_leproof · cited by 1
- Icc_isInteriorPoint_interiorproof · cited by 1
- IccLeftChart_applystatement · cited by 0
- IccLeftChart_symm_applystatement · cited by 0
- iccLeftChart_extend_zerostatement · cited by 0