Theorems · Theorem · global analysis
ModelWithCorners.isClosed_range
∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {E : Type u_2} [inst_1 : NormedAddCommGroup E]
[inst_2 : NormedSpace 𝕜 E] {H : Type u_3} [inst_3 : TopologicalSpace H] (I : ModelWithCorners 𝕜 E H),
IsClosed (Set.range ↑I)- Cited by
- 7 results in Mathlib
- Foundations
- Depth 153 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- Set.rangestatement · cited by 4,705
- ModelWithCornersstatement and proof · cited by 2,462
- IsClosedstatement · cited by 1,639
- ModelWithCorners.toFun'statement · cited by 373
- Topology.IsClosedEmbedding.isClosed_rangeproof · cited by 41
- ModelWithCorners.isClosedEmbeddingproof · cited by 6
Cited by7
Results whose statement or proof uses this declaration.
- ModelWithCorners.locallyCompactSpaceproof · cited by 5
- SmoothBumpFunction.isCompact_symm_image_closedBallproof · cited by 2
- ModelWithCorners.isInteriorPoint_or_isBoundaryPointproof · cited by 2
- SmoothBumpFunction.isClosed_image_of_isClosedproof · cited by 1
- MDifferentiableAt.isInteriorPoint_of_surjective_mfderivproof · cited by 1
- ModelWithCorners.mem_interior_range_of_mem_interior_range_of_mem_atlasproof · cited by 1
- ModelWithCorners.range_eq_closure_interiorproof · cited by 0