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Theorems · Theorem · general topology

TopologicalSpace.isOpen_sUnion

∀ {X : Type u} [self : TopologicalSpace X] (s : Set (Set X)),
  (∀ t ∈ s, TopologicalSpace.IsOpen t) → TopologicalSpace.IsOpen (⋃₀ s)

The union of a family of open sets is an open set. Use isOpen_sUnion in the root namespace instead.

Defined in
Mathlib.Topology.Defs.Basic
Cited by
1 results in Mathlib
Foundations
Depth 6 from the axioms · uses no axioms
Assumes
TopologicalSpace
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Around this declaration

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isOpen_sUnion · cited by 15isOpen_sUnionSet · cited by 53352SetTopologicalSpace · cited by 24529TopologicalSpaceSet.sUnion · cited by 392Set.sUnionTopologicalSpace.IsOpen · cited by 25TopologicalSpace.IsOpenTopologicalSpace.isOpen_sUnionCITED BYCITES

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Cited by1

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