Theorems · Theorem · dynamical systems
SymbolicDynamics.FullShift.isOpen_mulOccursInAt
∀ {A : Type u_1} [inst : TopologicalSpace A] [inst_1 : Inhabited A] {G : Type u_2} [inst_2 : Monoid G]
[IsLeftCancelMul G] [DiscreteTopology A] (p : SymbolicDynamics.FullShift.Pattern A G) (g : G),
IsOpen {x | p.mulOccursInAt x g}Occurrence sets are open.
- Defined in
- Mathlib.Dynamics.SymbolicDynamics.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 83 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
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.ofPredstatement · cited by 6,101
- Monoidstatement and proof · cited by 3,887
- IsOpenstatement and proof · cited by 2,400
- Finset.imageproof · cited by 910
- DiscreteTopologystatement and proof · cited by 373
- IsLeftCancelMulstatement and proof · cited by 51
- SymbolicDynamics.FullShift.Patternstatement and proof · cited by 21
- SymbolicDynamics.FullShift.Pattern.supportproof · cited by 13
- SymbolicDynamics.FullShift.Pattern.mulOccursInAtstatement · cited by 6
- SymbolicDynamics.FullShift.Pattern.mulShiftproof · cited by 4
- SymbolicDynamics.FullShift.isOpen_cylinderproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- SymbolicDynamics.FullShift.isClosed_mulForbiddenproof · cited by 0