Theorems · Theorem · general topology
Topology.WithLower.isOpen_preimage_ofLower
∀ {α : Type u_1} [inst : Preorder α] {s : Set α}, IsOpen (⇑Topology.WithLower.ofLower ⁻¹' s) ↔ IsOpen s- Cited by
- 0 results in Mathlib
- Foundations
- Depth 14 from the axioms · uses Quot.sound
- Assumes
- Preorder
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Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Setstatement and proof · cited by 53,352
- Equivstatement · cited by 8,337
- Preorderstatement and proof · cited by 7,952
- Set.preimagestatement · cited by 4,946
- IsOpenstatement · cited by 2,400
- Topology.WithLowerstatement · cited by 15
- Topology.WithLower.ofLowerstatement · cited by 9
- Topology.lowerstatement · cited by 7
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