Difference between revisions of "Pointed set"
From Encyclopedia of Mathematics
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| − | 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. | + | 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 algebra]]s, they are sets equipped with a single [[nullary operation]]. |
| − | The category of pointed sets has an initial and terminal object (cf. [[Null object of a category]]) consisting of a one-element set. | + | 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. |
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| + | 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==== | ====References==== | ||
| − | * S. MacLane, "Categories for the working mathematician" Graduate Texts in Mathematics '''5''', Springer (1971) ISBN 0-387-98403-8 | + | * S. MacLane, "Categories for the working mathematician" Graduate Texts in Mathematics '''5''', Springer (1971) {{ISBN|0-387-98403-8}} |
Latest revision as of 14:05, 19 November 2023
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.
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=34806
Pointed set. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Pointed_set&oldid=34806