instWithTopOfOrderTopology — Mathlib

English

For a,b in Topology.WithLowerSet α, ofLowerSet a ≤ ofLowerSet b ↔ a ⤳ b.

Русский

Для a,b в Topology.WithLowerSet α справедливо that ofLowerSet a ≤ ofLowerSet b эквивалентно a ⤳ b.

LaTeX

$$$\\forall {a b : Topology.WithLowerSet \\alpha},\\; ofLowerSet(a) \\le ofLowerSet(b) \\iff a \\curvearrowright b.$$$

Lean4

@[nolint unusedArguments]
instance [TopologicalSpace ι] [OrderTopology ι] : TopologicalSpace (WithTop ι) :=
  Preorder.topology _

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