chartedSpace_of_discreteTopology_chartAt

English

The product topology for charted spaces is the natural product of the component topologies.

Русский

Произведение топологий для charted spaces задаёт естественную топологию произведения.

LaTeX

$$instTopologicalSpaceModelPi ...$$

Lean4

/-- A chart on the discrete space is the constant chart. -/
@[simp, mfld_simps]
theorem chartedSpace_of_discreteTopology_chartAt [TopologicalSpace M] [TopologicalSpace H] [DiscreteTopology M]
    [h : Unique H] {x : M} :
    haveI := ChartedSpace.of_discreteTopology (M := M) (H := H)
    chartAt H x = OpenPartialHomeomorph.const (isOpen_discrete { x }) (isOpen_discrete { h.default }) :=
  rfl

Похожие утверждения