|
|
| Line 1: |
Line 1: |
| In [[mathematics]], a '''pointed set''' is a [[Set (mathematics)|set]] <math>X</math> with a distinguished element <math>x_0\in X</math>, which is called the '''basepoint'''. Maps of pointed sets ('''based maps''') are those [[function (mathematics)|functions]] that map one basepoint to another, i.e. a map <math>f : X \to Y</math> such that <math>f(x_0) = y_0</math>. This is usually denoted
| | I'm Luther but I never really liked that title. One of the things I adore most is climbing and now I have time to take on new issues. My job is a messenger. Her husband and her selected to reside in Alabama.<br><br>my page - extended car warranty - [http://magendoo.info/q/9138/crucial-knowledge-for-fixing-your-car-problems This Internet site] - |
| :<math>f : (X, x_0) \to (Y, y_0)</math>. | |
| | |
| Pointed sets may be regarded as a rather simple [[algebraic structure]]. In the sense of [[universal algebra]], they are structures with a single [[nullary operation]] which picks out the basepoint.
| |
| | |
| The [[Class (set theory)|class]] of all pointed sets together with the class of all based maps form a [[category theory|category]].
| |
| | |
| A pointed set may be seen as a [[pointed space]] under the [[discrete topology]] or as a [[vector space]] over the [[field with one element]].
| |
| | |
| There is a faithful functor from usual sets to pointed sets, but it is not full, and these categories are not equivalent.
| |
| | |
| == References ==
| |
| * {{cite book | title=An Introduction to Galois Cohomology and Its Applications | volume=377 | series=London Mathematical Society Lecture Note Series | author=Grégory Berhuy | publisher=Cambridge University Press | year=2010 | isbn=0-521-73866-0 | page=34 }}
| |
| * {{cite book
| |
| |last=Mac Lane
| |
| |first=Saunders
| |
| |authorlink=Saunders Mac Lane
| |
| |title=[[Categories for the Working Mathematician]]
| |
| |publisher=Springer-Verlag
| |
| |year=1998
| |
| |edition=2nd
| |
| |isbn=0-387-98403-8
| |
| }}
| |
| | |
| {{DEFAULTSORT:Pointed Set}}
| |
| [[Category:Basic concepts in set theory]]
| |
| [[Category:Abstract algebra]]
| |
Latest revision as of 07:29, 6 January 2015
I'm Luther but I never really liked that title. One of the things I adore most is climbing and now I have time to take on new issues. My job is a messenger. Her husband and her selected to reside in Alabama.
my page - extended car warranty - This Internet site -