Theorems · Theorem · dynamical systems
SymbolicDynamics.FullShift.isClosed_occursInAt
∀ {A : Type u_1} [inst : TopologicalSpace A] [inst_1 : Inhabited A] {G : Type u_2} [inst_2 : AddMonoid G]
[IsLeftCancelAdd G] [T1Space A] (p : SymbolicDynamics.FullShift.Pattern A G) (g : G), IsClosed {x | p.occursInAt x g}Occurrence sets are closed.
- Defined in
- Mathlib.Dynamics.SymbolicDynamics.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 85 from the axioms · uses propext, Classical.choice, Quot.sound
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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
- AddMonoidstatement and proof · cited by 2,864
- IsClosedstatement and proof · cited by 1,639
- Finset.imageproof · cited by 910
- T1Spacestatement and proof · cited by 275
- IsLeftCancelAddstatement and proof · cited by 72
- SymbolicDynamics.FullShift.Patternstatement and proof · cited by 21
- SymbolicDynamics.FullShift.Pattern.supportproof · cited by 13
- SymbolicDynamics.FullShift.Pattern.occursInAtstatement · cited by 6
- SymbolicDynamics.FullShift.Pattern.shiftproof · cited by 4
- SymbolicDynamics.FullShift.isClosed_cylinderproof · cited by 2
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