# Pointed set

From Encyclopedia of Mathematics

2010 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.

#### References

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

**How to Cite This Entry:**

Pointed set.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Pointed_set&oldid=39756