Theorems · Theorem · general topology

isBounded_pow

∀ {R : Type u_2} [inst : Bornology R] [inst_1 : Monoid R] [BoundedMul R] {s : Set R},
  Bornology.IsBounded s → ∀ (n : ℕ), Bornology.IsBounded ((fun x => x ^ n) '' s)

Defined in: Mathlib.Topology.Bornology.BoundedOperation
Cited by: 0 results in Mathlib
Foundations: Depth 70 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Bornology Monoid BoundedMul

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Setstatement and proof · cited by 53,352
Set.imagestatement and proof · cited by 5,609
Monoidstatement and proof · cited by 3,887
pow_zeroproof · cited by 1,094
Set.image_congrproof · cited by 533
pow_succproof · cited by 374
Bornology.IsBoundedstatement and proof · cited by 293
Bornologystatement and proof · cited by 188
Set.image_emptyproof · cited by 73
Bornology.IsBounded.subsetproof · cited by 45
Set.Nonempty.image_constproof · cited by 26
Set.mul_mem_mulproof · cited by 22

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