Theorems · Theorem · general topology

tendsto_nhds_unique_inseparable

∀ {X : Type u_1} {Y : Type u_2} [inst : TopologicalSpace X] [R1Space X] {f : Y → X} {l : Filter Y} {a b : X} [l.NeBot],
  Filter.Tendsto f l (nhds a) → Filter.Tendsto f l (nhds b) → Inseparable a b

Limits are unique up to separability. A weaker version of tendsto_nhds_unique for R1Space.

Defined in

Mathlib.Topology.Separation.Basic

Cited by

10 results in Mathlib

Foundations

Depth 68 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceR1SpaceFilter.NeBot