A continuous injective map that is either open or closed is a topological embedding.

Proof
The proof uses (0x677bc58f) . Before this result can be applied we need to show that the restriction to the image is continuous and that the property of being open or closed is conserved. The first part follows from (0x6792a06a) .
Remarks
  • The condition is not sufficient. There are examples where topological embeddings are neither open nor closed.