Theorems · Theorem · general topology

ClusterPt.map

∀ {X : Type u_1} {Y : Type u_2} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y] {f : X → Y} {x : X}
  {lx : Filter X} {ly : Filter Y}, ClusterPt x lx → ContinuousAt f x → Filter.Tendsto f lx ly → ClusterPt (f x) ly

Defined in

Mathlib.Topology.Continuous

Cited by

4 results in Mathlib

Foundations

Depth 67 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceTopologicalSpace