[[Topology MOC]]
# Local injection

A continuous map $f : X \to Y$ between topological spaces is **locally injective at a point** $x \in X$ if $x$ has an (open) neighbourhood $U$ such that $f \restriction U$ is an [[Surjectivity, injectivity, and bijectivity|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]]

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