Theorems · Theorem · general topology

Homeomorph.isOpen_preimage

∀ {X : Type u_1} {Y : Type u_2} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y] (h : X ≃ₜ Y) {s : Set Y},
  IsOpen (⇑h ⁻¹' s) ↔ IsOpen s

Defined in

Mathlib.Topology.Homeomorph.Defs

Cited by

7 results in Mathlib

Foundations

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

Assumes

TopologicalSpaceTopologicalSpace