Theorems · Theorem · manifolds
ChartedSpace.t1Space
∀ (H : Type u) (M : Type u_2) [inst : TopologicalSpace H] [inst_1 : TopologicalSpace M] [ChartedSpace H M] [T1Space H], T1Space M
A charted space over a T1 space is T1. Note that this is not true for T2 (for instance for the real line with a double origin).
- Defined in
- Mathlib.Geometry.Manifold.ChartedSpace
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 89 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.
- TopologicalSpacestatement and proof · cited by 24,529
- Set.preimageproof · cited by 4,946
- Compl.complproof · cited by 2,925
- ChartedSpacestatement and proof · cited by 2,397
- PartialEquiv.sourceproof · cited by 964
- PartialHomeomorph.toPartialEquivproof · cited by 917
- OpenPartialHomeomorph.toPartialHomeomorphproof · cited by 851
- OpenPartialHomeomorph.toFun'proof · cited by 745
- chartAtproof · cited by 301
- T1Spacestatement and proof · cited by 275
- OpenPartialHomeomorph.open_sourceproof · cited by 65
- isOpen_compl_singletonproof · cited by 27
Cited by1
Results whose statement or proof uses this declaration.
- ModelWithCorners.t1Spaceproof · cited by 5