Theorems · Theorem · general topology

Continuous.subtype_map

∀ {X : Type u} {Y : Type v} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y] {p : X → Prop} {f : X → Y},
  Continuous f → ∀ {q : Y → Prop} (hpq : ∀ (x : X), p x → q (f x)), Continuous (Subtype.map f hpq)

Defined in

Mathlib.Topology.Constructions

Cited by

3 results in Mathlib

Foundations

Depth 72 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceTopologicalSpace