Theorems · Theorem · number theory
IsZLattice.isCompact_range_of_periodic
∀ {E : Type u_1} {F : Type u_2} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E] [FiniteDimensional ℝ E]
[inst_3 : TopologicalSpace F] (L : Submodule ℤ E) [inst_4 : DiscreteTopology ↥L] [IsZLattice ℝ L] (f : E → F),
Continuous f → (∀ (z w : E), w ∈ L → f (z + w) = f z) → IsCompact (Set.range f)If f is periodic wrt a ℤ-lattice, then the range of f is compact.
- Defined in
- Mathlib.Algebra.Module.ZLattice.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 181 from the axioms · uses propext, Classical.choice, Quot.sound
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