instBoundedLENhdsClassOrderDual — Mathlib

English

Finite index Pi-space inherits the bounded generator neighborhood class from its factors: if ι is finite and each π(i) is Preorder, TopologicalSpace, and BoundGENhdsClass, then the Pi-space ∀ i, π(i) has BoundGENhdsClass.

Русский

Если ι конечен и каждый π(i) является упорядоченным топологическим пространством с BoundGENhdsClass, то Pi-пространство имеет BoundGENhdsClass.

LaTeX

$$$ [Finite ι] [∀ i, Preorder (π i)] [∀ i, TopologicalSpace (π i)] [∀ i, BoundGENhdsClass (π i)] : BoundGENhdsClass (∀ i, π i). $$$

Lean4

instance : BoundedLENhdsClass αᵒᵈ :=
  ⟨@isBounded_ge_nhds α _ _ _⟩

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