closed complex plane
is open but not closed, since it doesn’t contain the accumulation points of all sets of complex numbers, for example of the set . One can to the closed complex plane by adding to the infinite point which the lacking accumulation points. One settles that , where the latter means the real infinity.
The resulting space is the one-point compactification of . The open sets are the open sets in together with sets containing whose complement is compact in . Conceptually, one thinks of the additional open sets as those open sets “around ”.
The one-point compactification of is also the complex projective line , as well as the Riemann sphere.
|Title||closed complex plane|
|Date of creation||2013-03-22 17:37:48|
|Last modified on||2013-03-22 17:37:48|
|Last modified by||pahio (2872)|
|Synonym||extended complex plane|