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Theorems · Theorem · general topology

continuous_sumElim

∀ {X : Type u} {Y : Type v} {Z : Type u_2} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y]
  [inst_2 : TopologicalSpace Z] {f : X → Z} {g : Y → Z}, Continuous (Sum.elim f g) ↔ Continuous f ∧ Continuous g
Defined in
Mathlib.Topology.Constructions.SumProd
Cited by
2 results in Mathlib
Foundations
Depth 72 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
TopologicalSpaceTopologicalSpaceTopologicalSpace
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Continuous.sumElim · cited by 7Continuous.sumElimcontinuous_sumMap · cited by 1continuous_sumMapTopologicalSpace · cited by 24529TopologicalSpaceContinuous · cited by 2592Continuouscontinuous_sum_dom · cited by 3continuous_sum_domcontinuous_sumElimCITED BYCITES

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Cited by2

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