| topology - HighBeam Encyclopedia |

| | A continuous transformation, also called a topological transformation or homeomorphism, is a one-to-one correspondence between the **points** of one figure and the **points** of another figure such that **points** that are arbitrarily close on one figure are transformed into **points** that are also arbitrarily close on the other figure. |

| | If V is the number of **points** (vertices) in the decomposition, E is the number of line segments (edges), and F is the number of regions (faces), then the characteristic is given by Χ= V - E + F and is the same for all possible polyhedral decomposition of the given surface. |

| | Closely related to the Euler-Poincaré characteristic is the connectivity number of a surface, which is equal to the largest number of closed cuts (or cuts connecting **points** on boundaries or on previous cuts) that can be made on the surface without separating it into two or more parts. |

| www.encyclopedia.com /html/t/topology.asp (1070 words) |