Theorems · Theorem · general topology
isBounded_nsmul
∀ {R : Type u_2} [inst : Bornology R] [inst_1 : AddMonoid R] [BoundedAdd R] {s : Set R},
Bornology.IsBounded s → ∀ (n : ℕ), Bornology.IsBounded ((fun x => n • x) '' s)- Cited by
- 0 results in Mathlib
- Foundations
- Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- BornologyAddMonoidBoundedAdd
Around this declaration
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Cites18
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Set.imagestatement and proof · cited by 5,609
- AddMonoidstatement and proof · cited by 2,864
- Set.image_congrproof · cited by 533
- Bornology.IsBoundedstatement and proof · cited by 293
- Bornologystatement and proof · cited by 188
- zero_nsmulproof · cited by 137
- Set.mem_imageproof · cited by 131
- Set.nonempty_iff_ne_emptyproof · cited by 96
- Set.image_emptyproof · cited by 73
- succ_nsmulproof · cited by 65
- Bornology.IsBounded.subsetproof · cited by 45
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