Pointed set

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2020 Mathematics Subject Classification: Primary: 03E [MSN][ZBL]

A non-empty set having a distinguished point or "base point". Maps of pointed sets are maps of the underlying sets that preserve the base point. As universal algebras, they are sets equipped with a single nullary operation.

The category of pointed sets and base-point preserving maps has an initial and terminal object (cf. Null object of a category) consisting of a one-element set.

For topological spaces with a distinguished point, see Pointed space. For the categorical construction generalising the relationship between sets and pointed sets, see Pointed object.


  • S. MacLane, "Categories for the working mathematician" Graduate Texts in Mathematics 5, Springer (1971) ISBN 0-387-98403-8
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