Mathlib Map

Theorems · Theorem · general topology

Topology.IsInducing.noetherianSpace

∀ {α : Type u_1} {β : Type u_2} [inst : TopologicalSpace α] [inst_1 : TopologicalSpace β]
  [TopologicalSpace.NoetherianSpace α] {i : β → α}, Topology.IsInducing i → TopologicalSpace.NoetherianSpace β
Defined in
Mathlib.Topology.NoetherianSpace
Cited by
1 results in Mathlib
Foundations
Depth 82 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
TopologicalSpaceTopologicalSpaceTopologicalSpace.NoetherianSpace
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

TopologicalSpace.NoetherianSpace.of_subset · cited by 2NoetherianSpace.of_subsetTopologicalSpace · cited by 24529TopologicalSpaceSetLike.coe · cited by 8199SetLike.coeSet.image · cited by 5609Set.imageTopologicalSpace.Opens · cited by 2040TopologicalSpace.OpensTopology.IsInducing · cited by 266Topology.IsInducingTopologicalSpace.NoetherianSpace · cited by 23TopologicalSpace.Noetheri…Topology.IsInducing.isCompact_iff · cited by 9IsInducing.isCompact_iffTopologicalSpace.NoetherianSpace.isCompact · cited by 5NoetherianSpace.isCompactTopologicalSpace.noetherianSpace_iff_opens · cited by 3TopologicalSpace.noetheri…IsInducing.noetherianSpaceCITED BYCITES

Cites9

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by1

Results whose statement or proof uses this declaration.