Difference between revisions of "Topology"
Jump to navigation
Jump to search
(New page: Topology is a branch of advanced mathematics that focuses on sets and the manipulation and mapping of sets. General topology was traditionally subdivided into: *continuous topology *geom...) |
|||
| Line 10: | Line 10: | ||
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 sets 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. | ||
| + | |||
[[category:mathematics]] | [[category:mathematics]] | ||
Revision as of 12:37, October 1, 2007
Topology is a branch of advanced mathematics that focuses on sets and the manipulation and mapping of sets. General topology was traditionally subdivided into:
- continuous topology
- geometric topology
More recently the subject topology is divided into:
- algebraic topology
- point set topology
Topology also has a specific mathematical definition as a collection of open sets 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.