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...)
 
(genus of a surface - an obscure idea that need not distract us from Genus and Species)
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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.