# Difference between revisions of "Topology"

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(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...) |
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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]]. | ||

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+ | 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. | ||

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[[category:mathematics]] | [[category:mathematics]] |

## Revision as of 06:37, 1 October 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.