Theorems · Theorem · dynamical systems
Function.HasCompactFixedSupport.comp
∀ {X : Type u_1} [inst : TopologicalSpace X] {f g : X → X},
Function.HasCompactFixedSupport f → Function.HasCompactFixedSupport g → Function.HasCompactFixedSupport (f ∘ g)If f and g have compact fixed support, then so does their composition f ∘ g.
- Defined in
- Mathlib.Dynamics.FixedPoints.Support
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 85 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- TopologicalSpace
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Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- Compl.complproof · cited by 2,925
- le_reflproof · cited by 2,061
- IsClosedproof · cited by 1,639
- IsCompactproof · cited by 1,282
- le_imp_le_of_le_of_leproof · cited by 576
- Function.fixedPointsproof · cited by 90
- Set.union_subset_unionproof · cited by 29
- Set.compl_interproof · cited by 26
- IsCompact.unionproof · cited by 23
- IsClosed.unionproof · cited by 17
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