Theorems · Theorem · general topology

IsOpen.preimage

∀ {X : Type u_1} {Y : Type u_2} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y] {f : X → Y},
  Continuous f → ∀ {t : Set Y}, IsOpen t → IsOpen (f ⁻¹' t)

Defined in

Mathlib.Topology.Continuous

Cited by

147 results in Mathlib

Foundations

Depth 6 from the axioms, rests on 12 definitions · uses no axioms

Assumes

TopologicalSpaceTopologicalSpace