Theorems · Theorem · measure theory
Real.dimH_of_mem_nhds
∀ {E : Type u_4} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E] [FiniteDimensional ℝ E] {x : E} {s : Set E},
s ∈ nhds x → dimH s = ↑(Module.finrank ℝ E)- Cited by
- 3 results in Mathlib
- Foundations
- Depth 253 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites28
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Setstatement and proof · cited by 53,352
- Realstatement and proof · cited by 25,697
- RingHom.idproof · cited by 18,349
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- ENNRealstatement and proof · cited by 9,879
- Filterstatement and proof · cited by 8,121
- Set.imageproof · cited by 5,609
- nhdsstatement and proof · cited by 5,554
- le_antisymmproof · cited by 2,068
- FiniteDimensionalstatement and proof · cited by 1,854
Cited by3
Results whose statement or proof uses this declaration.
- Real.dimH_univ_eq_finrankproof · cited by 4
- dense_compl_of_dimH_lt_finrankproof · cited by 2
- Real.dimH_of_nonempty_interiorproof · cited by 1