instQuasiCompactOfUniversallyClosed

English

UniversallyInjective is closed under composition: if f and g have UniversallyInjective, then their composition f ∘ g also has UniversallyInjective.

Русский

UniversallyInjective замкнуто относительно композиции: если f и g имеют UniversalInjective, то и их композиция f ∘ g обладает этим свойством.

LaTeX

$$$\forall X\;Y\;Z\; (f:X\to Y)\; (g:Y\to Z), \; \operatorname{UniversallyInjective}(f) \land \operatorname{UniversallyInjective}(g) \Rightarrow \operatorname{UniversallyInjective}(f\circ g).$$$

Lean4

instance (priority := 900) [UniversallyClosed f] : QuasiCompact f where
  isCompact_preimage _ _ := f.isProperMap.isCompact_preimage

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