Changes

Topology is a branch of advanced mathematics that focuses on sets and the manipulation and mapping of sets.  General topology was traditionally subdivided into:

'''Topology''' is a branch of advanced [[mathematics]] that focuses on [[set]]s and the manipulation and [[mapping]] of sets.  General topology was traditionally subdivided into:

*continuous topology

*continuous topology

More recently the subject topology is divided into:

More recently the subject topology is divided into:

*algebraic topology

*[[algebraic topology]]

*point set topology

*[[point-set topology]]

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

Topology also has a specific mathematical definition as a collection of [[open set]]s in a [[topological space]]. The open sets can be manipulated, forming the [[basis]] of the topology. The opposite of open sets are [[closed set]]s. Topology may also be defined in terms of closed sets, but this yields an [[equivalence relation|equivalent]] definition.

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.  

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.