of_closedIciTopology — Mathlib

English

Already covered: product of two BoundGENhds spaces retains BoundGENhdsClass.

Русский

Уже рассмотрено: произведение двух пространств с BoundGENhds сохраняет свойство.

LaTeX

$$$ (\text{Prod.instBoundedGENhdsClass}) : BoundedGENhdsClass (\alpha \times \beta). $$$

Lean4

instance (priority := 100) of_closedIciTopology [LinearOrder α] [TopologicalSpace α] [ClosedIciTopology α] :
    BoundedLENhdsClass α :=
  ⟨fun a ↦ ((isTop_or_exists_gt a).elim fun h ↦ ⟨a, Eventually.of_forall h⟩) <| Exists.imp fun _b ↦ eventually_le_nhds⟩
    -- See note [lower instance priority]

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