Mathlib Map

Theorems · Theorem · general topology

OnePoint.nhds_coe_eq

∀ {X : Type u_1} [inst : TopologicalSpace X] (x : X), nhds ↑x = Filter.map OnePoint.some (nhds x)
Defined in
Mathlib.Topology.Compactification.OnePoint.Basic
Cited by
2 results in Mathlib
Foundations
Depth 93 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
TopologicalSpace
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

OnePoint.not_continuous_cofiniteTopology_of_symm · cited by 1OnePoint.not_continuous_c…OnePoint.continuousAt_coe · cited by 0OnePoint.continuousAt_coeTopologicalSpace · cited by 24529TopologicalSpaceFilter · cited by 8121Filternhds · cited by 5554nhdsFilter.map · cited by 819Filter.mapOnePoint · cited by 126OnePointOnePoint.some · cited by 76OnePoint.someTopology.IsOpenEmbedding.map_nhds_eq · cited by 22IsOpenEmbedding.map_nhds_…OnePoint.isOpenEmbedding_coe · cited by 9OnePoint.isOpenEmbedding_…OnePoint.nhds_coe_eqCITED BYCITES

Cites8

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

Cited by2

Results whose statement or proof uses this declaration.