Theorems · Theorem · functional analysis
interior_subset_gauge_lt_one
∀ {E : Type u_2} [inst : AddCommGroup E] [inst_1 : Module ℝ E] [inst_2 : TopologicalSpace E] [ContinuousSMul ℝ E]
(s : Set E), interior s ⊆ {x | gauge s x < 1}- Defined in
- Mathlib.Analysis.Convex.Gauge
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 119 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites36
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 · cited by 6,101
- nhdsproof · cited by 5,554
- Set.preimageproof · cited by 4,946
- Filter.Tendstoproof · cited by 3,814
- Filter.Eventuallyproof · cited by 3,134
- LT.lt.leproof · cited by 2,189
- nhdsWithinproof · cited by 1,912
Cited by5
Results whose statement or proof uses this declaration.
- setOfPred_gauge_lt_one_eq_self_of_isOpenproof · cited by 4
- gauge_lt_one_of_mem_of_isOpenproof · cited by 3
- setOfPred_gauge_lt_one_eq_interiorproof · cited by 3
- mapsTo_gaugeRescale_interiorproof · cited by 1
- mem_frontier_of_gauge_eq_oneproof · cited by 0