Thomson's lamp

In mathematics, a pointed set is a set $X$ with a distinguished element $x_{0}\in X$, which is called the basepoint. Maps of pointed sets (based maps) are those functions that map one basepoint to another, i.e. a map $f:X\to Y$ such that $f(x_{0})=y_{0}$. This is usually denoted

$f:(X,x_{0})\to (Y,y_{0})$.

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 of all pointed sets together with the class of all based maps form a 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

• 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.
  
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• 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.
  
  My blog: http://www.primaboinca.com/view_profile.php?userid=5889534