topology of the complex plane
for . Here, is the complex modulus (http://planetmath.org/ModulusOfComplexNumber).
If we identify and , it is clear that the above topology coincides with topology induced by the Euclidean metric on .
Some basic topological concepts for :
A point is an accumulation point of a subset of , if any open disk contains at least one point of distinct from .
A point is an interior point of the set , if there exists an open disk which is contained in .
A set is open, if each of its points is an interior point of .
A set is closed, if all its accumulation points belong to .
A set is bounded, if there is an open disk containing .
A set is compact, if it is closed and bounded.
|Title||topology of the complex plane|
|Date of creation||2013-03-22 13:38:40|
|Last modified on||2013-03-22 13:38:40|
|Last modified by||matte (1858)|