Mathlib Map

Theorems · Theorem · general topology

IsOpenMap.map_nhds_eq

∀ {X : Type u_1} {Y : Type u_2} {f : X → Y} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y],
  IsOpenMap f → ∀ {x : X}, ContinuousAt f x → Filter.map f (nhds x) = nhds (f x)
Defined in
Mathlib.Topology.Maps.Basic
Cited by
1 results in Mathlib
Foundations
Depth 62 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
TopologicalSpaceTopologicalSpace
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Around this declaration

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

IsOpenMap.map_nhdsSet_eq · cited by 0IsOpenMap.map_nhdsSet_eqTopologicalSpace · cited by 24529TopologicalSpaceFilter · cited by 8121Filternhds · cited by 5554nhdsle_antisymm · cited by 2068le_antisymmFilter.map · cited by 819Filter.mapContinuousAt · cited by 697ContinuousAtIsOpenMap · cited by 253IsOpenMapIsOpenMap.nhds_le · cited by 11IsOpenMap.nhds_leIsOpenMap.map_nhds_eqCITED BYCITES

Cites8

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Cited by1

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