preimageSingletonHomeomorph — Mathlib

English

Same as 203550; equivalence of tendsto with base projection and fiber component.

Русский

Тождество сходимости через проекцию и волокно.

LaTeX

$$$ \text{theorem } Tendsto\ f\ l\ (nhds\ z) \iff \dots $$$

Lean4

/-- Each fiber of a trivialization is homeomorphic to the specified fiber. -/
def preimageSingletonHomeomorph {b : B} (hb : b ∈ e.baseSet) : proj ⁻¹' { b } ≃ₜ F :=
  .trans (e.preimageHomeomorph (Set.singleton_subset_iff.mpr hb)) <|
    .trans (.prodCongr (Homeomorph.homeomorphOfUnique ({ b } : Set B) PUnit.{1}) (Homeomorph.refl F))
      (Homeomorph.punitProd F)

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