Theorems · Theorem · general topology

Homeomorph.isClosed_setOfPred_iff

∀ {X : Type u_1} {Y : Type u_2} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y] {p : X → Prop} {q : Y → Prop}
  (f : X ≃ₜ Y), IsClopen {x | p x} → IsClopen {y | q y} → IsClosed {x | p x ↔ q (f x)}

Defined in

Mathlib.Topology.Homeomorph.Defs

Cited by

3 results in Mathlib

Foundations

Depth 75 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceTopologicalSpace