continuousMul_of_discreteTopology

English

If N is equipped with the discrete topology, then any multiplication map (hence in particular multiplication) is continuous; i.e., a discrete topological space makes every algebraic operation continuous.

Русский

Если у пространства N задан дискретный топологический структура, то любая операция умножения неприменима, т.е. непрерывна.

LaTeX

$$$[TopologicalSpace\\,N] \\land [Mul\\,N] \\land [DiscreteTopology\\,N] \\Rightarrow \\text{ContinuousMul}\\,N$$$

Lean4

@[to_additive]
instance (priority := 100) continuousMul_of_discreteTopology [TopologicalSpace N] [Mul N] [DiscreteTopology N] :
    ContinuousMul N :=
  ⟨continuous_of_discreteTopology⟩

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