Topology MOC

Local injection

A continuous map 𝑓 :𝑋 →𝑌 between topological spaces is locally injective at a point 𝑥 ∈𝑋 if 𝑥 has an (open) neighbourhood 𝑈 such that 𝑓 ↾𝑈 is an injection. It is locally injective if it is locally injective at every point. #m/def/topology

Properties

• Every injection between topological spaces is a local injection
• Every fibre of a local injection is discrete

#state/tidy | #lang/en | #SemBr