Changes

*point set topology

*point set topology

Topology also has a specific mathematical definition as a collection of open sets in a [[topological space]].

Topology also has a specific mathematical definition as a collection of [[open set]]s in a [[topological space]].

In topology, a ''genus'' of a surface is the greatest number of distinct, continuous closed curves that may be drawn on it without separating the surface into distinct regions.  The closed curves cannot be self-intersecting.  The genus of the surface of a sphere is 0, while the genus of a doughnut shape is 1.  

In topology, a ''genus'' of a surface is the greatest number of distinct, [[continuous]] [[closed_set|closed]] [[curve]]s that may be drawn on it without separating the surface into distinct regions.  The closed curves cannot be self-intersecting.  The genus of the surface of a [[sphere]] is 0, while the genus of a doughnut shape is 1.  

If you draw a circle on a sphere, then you can put a point A inside the circle and a point B outside the circle. The only way to connect A to B would have to cross the circle. So drawing the circle divides the surface of the sphere into two regions. But you can draw a circle around the edge (rim) of a doughnut without creating two regions. You can get from point A on one side of the line to point B on the other side, by going through the hole in the center.  

If you draw a circle on a sphere, then you can put a point A inside the circle and a point B outside the circle. The only way to connect A to B would have to cross the circle. So drawing the circle divides the surface of the sphere into two regions. But you can draw a circle around the edge (rim) of a doughnut without creating two regions. You can get from point A on one side of the line to point B on the other side, by going through the hole in the center.  

[[category:mathematics]]

[[category:mathematics]]