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. topology

Properties

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

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