Theorems · Theorem · dynamical systems
SymbolicDynamics.FullShift.isClosed_cylinder
∀ {A : Type u_1} {G : Type u_2} [inst : TopologicalSpace A] [T1Space A] (U : Finset G) (x : G → A),
IsClosed (SymbolicDynamics.FullShift.cylinder U x)Cylinders are closed when A is a T1 Space.
- Defined in
- Mathlib.Dynamics.SymbolicDynamics.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 84 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- TopologicalSpaceT1Space
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- Finsetstatement and proof · cited by 13,712
- IsClosedstatement and proof · cited by 1,639
- T1Spacestatement and proof · cited by 275
- SymbolicDynamics.FullShift.cylinderstatement · cited by 6
- isClosed_set_piproof · cited by 5
- SymbolicDynamics.FullShift.cylinder_eq_set_piproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- SymbolicDynamics.FullShift.isClosed_occursInAtproof · cited by 0
- SymbolicDynamics.FullShift.isClosed_mulOccursInAtproof · cited by 0