Theorems · Theorem · general topology
lowerClosure_interior_subset
∀ {α : Type u_1} [inst : NormedAddCommGroup α] [inst_1 : Preorder α] [IsOrderedAddMonoid α] (s : Set α),
↑(lowerClosure (interior s)) ⊆ interior ↑(lowerClosure s)- Defined in
- Mathlib.Analysis.Normed.Order.UpperLower
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 163 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites13
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
- NormedAddCommGroupstatement and proof · cited by 15,752
- SetLike.coestatement · cited by 8,199
- Preorderstatement and proof · cited by 7,952
- IsOrderedAddMonoidstatement and proof · cited by 1,659
- interiorstatement · cited by 714
- LowerSetstatement · cited by 230
- lowerClosurestatement and proof · cited by 83
- interior_monoproof · cited by 38
- LowerSet.lowerproof · cited by 13
- subset_lowerClosureproof · cited by 12
- lowerClosure_minproof · cited by 6
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