| | 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. |
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