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Theorems · Theorem · general topology

generateFrom_insert_of_generateOpen

∀ {α : Type u_1} {s : Set (Set α)} {t : Set α},
  TopologicalSpace.GenerateOpen s t → TopologicalSpace.generateFrom (insert t s) = TopologicalSpace.generateFrom s
Defined in
Mathlib.Topology.Order
Cited by
2 results in Mathlib
Foundations
Depth 62 from the axioms · uses propext, Classical.choice, Quot.sound
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

generateFrom_insert_univ · cited by 1generateFrom_insert_univgenerateFrom_insert_empty · cited by 0generateFrom_insert_emptySet · cited by 53352SetTopologicalSpace · cited by 24529TopologicalSpacele_antisymm · cited by 2068le_antisymmSet.subset_insert · cited by 96Set.subset_insertTopologicalSpace.generateFrom · cited by 62TopologicalSpace.generate…TopologicalSpace.GenerateOpen · cited by 12TopologicalSpace.Generate…TopologicalSpace.isOpen_generateFrom_of_mem · cited by 11TopologicalSpace.isOpen_g…le_generateFrom · cited by 10le_generateFromTopologicalSpace.generateFrom_anti · cited by 6TopologicalSpace.generate…generateFrom_insert_of_genera…CITED BYCITES

Cites9

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Cited by2

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