Theorems · Theorem · functional analysis
IsClosed.balancedCore
∀ {𝕜 : Type u_1} {E : Type u_2} [inst : NormedDivisionRing 𝕜] [inst_1 : AddCommGroup E] [inst_2 : Module 𝕜 E]
[inst_3 : TopologicalSpace E] [ContinuousSMul 𝕜 E] {U : Set E}, IsClosed U → IsClosed (balancedCore 𝕜 U)- Cited by
- 1 results in Mathlib
- Foundations
- Depth 121 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
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
- TopologicalSpacestatement and proof · cited by 24,529
- Modulestatement and proof · cited by 20,661
- AddCommGroupstatement and proof · cited by 12,871
- Norm.normproof · cited by 5,413
- Set.Nonemptyproof · cited by 2,627
- IsClosedstatement and proof · cited by 1,639
- ContinuousSMulstatement and proof · cited by 1,016
- zero_lt_oneproof · cited by 598
- lt_of_lt_of_leproof · cited by 438
- NormedDivisionRingstatement and proof · cited by 360
- norm_pos_iffproof · cited by 168
Cited by1
Results whose statement or proof uses this declaration.
- nhds_basis_closed_balancedproof · cited by 0