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Theorems · Theorem · general topology

continuous_sum_dom

∀ {X : Type u} {Y : Type v} {Z : Type u_2} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y]
  [inst_2 : TopologicalSpace Z] {f : X ⊕ Y → Z}, Continuous f ↔ Continuous (f ∘ Sum.inl) ∧ Continuous (f ∘ Sum.inr)
Defined in
Mathlib.Topology.Constructions.SumProd
Cited by
3 results in Mathlib
Foundations
Depth 71 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
TopologicalSpaceTopologicalSpaceTopologicalSpace
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Around this declaration

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continuous_sumElim · cited by 2continuous_sumElimcontinuous_isRight · cited by 0continuous_isRightcontinuous_isLeft · cited by 0continuous_isLeftTopologicalSpace · cited by 24529TopologicalSpaceContinuous · cited by 2592ContinuousIff.and · cited by 33Iff.andcontinuous_coinduced_dom · cited by 13continuous_coinduced_domcontinuous_sup_dom · cited by 1continuous_sup_domcontinuous_sum_domCITED BYCITES

Cites5

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Cited by3

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