Theorems · Theorem · general topology

DenseRange.dense_of_mapsTo

∀ {X : Type u_1} {Y : Type u_2} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y] {s : Set X} {f : X → Y},
  DenseRange f → Continuous f → Dense s → ∀ {t : Set Y}, Set.MapsTo f s t → Dense t

If a continuous map with dense range maps a dense set to a subset of t, then t is a dense set.

Defined in

Mathlib.Topology.Continuous

Cited by

2 results in Mathlib

Foundations

Depth 79 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceTopologicalSpace