toTopologicalSpace_injective — Mathlib

English

The forgetful functor from RingTopology to the underlying TopologicalSpace is injective; i.e., the topology determines the RingTopology uniquely.

Русский

Функтор забывания от RingTopology до базовой топологии инъективен; топология однозначно определяет RingTopology.

LaTeX

$$toTopologicalSpace_injective$$

Lean4

theorem toTopologicalSpace_injective : Injective (toTopologicalSpace : RingTopology R → TopologicalSpace R) := by
  intro f g _; cases f; cases g; congr

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