English
There is a canonical ring homomorphism from the stalk to R, given by evaluating sections at the distinguished base point.
Русский
Существует канонический кольцевой гомоморфизм от stalk к R, задаваемый оценкой секций в указанной базовой точке.
LaTeX
$$$$ \\mathrm{evalHom}(x) : (\\mathcal{O}_x) \\to R $$$$
Lean4
/-- A fiber bundle `E` over a base `B` with model fiber `F` is naturally a charted space modelled on
`B × F`. -/
instance chartedSpace' : ChartedSpace (B × F) (TotalSpace F E)
where
atlas := (fun e : Trivialization F (π F E) => e.toOpenPartialHomeomorph) '' trivializationAtlas F E
chartAt x := (trivializationAt F E x.proj).toOpenPartialHomeomorph
mem_chart_source x := (trivializationAt F E x.proj).mem_source.mpr (mem_baseSet_trivializationAt F E x.proj)
chart_mem_atlas _ := mem_image_of_mem _ (trivialization_mem_atlas F E _)
