Theorems · Theorem · functional analysis
setOfPred_gauge_lt_one_eq_self_of_isOpen
∀ {E : Type u_2} [inst : AddCommGroup E] [inst_1 : Module ℝ E] {s : Set E} [inst_2 : TopologicalSpace E]
[ContinuousSMul ℝ E], Convex ℝ s → 0 ∈ s → IsOpen s → {x | gauge s x < 1} = s- Defined in
- Mathlib.Analysis.Convex.Gauge
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 162 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
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
- Realstatement and proof · cited by 25,697
- TopologicalSpacestatement and proof · cited by 24,529
- Modulestatement and proof · cited by 20,661
- AddCommGroupstatement and proof · cited by 12,871
- Set.ofPredstatement and proof · cited by 6,101
- IsOpenstatement and proof · cited by 2,400
- ContinuousSMulstatement and proof · cited by 1,016
- interiorproof · cited by 714
- Convexstatement and proof · cited by 551
- LE.le.antisymmproof · cited by 507
- IsOpen.mem_nhdsproof · cited by 470
Cited by4
Results whose statement or proof uses this declaration.
- gaugeSeminormFamily_ballproof · cited by 1
- gaugeSeminorm_ball_oneproof · cited by 0
- gauge_lt_one_eq_self_of_isOpenproof · cited by 0
- setOf_gauge_lt_one_eq_self_of_isOpenproof · cited by 0