Let be a local complex analytic variety. A function (where is open in ) is said to be weakly holomorphic through if there exists a nowhere dense complex analytic subvariety and contains the singular points of and , and such that is holomorphic on and is locally bounded on .
It is not hard to show that we can then just take to be the set of singular points of and have as we can extend to all the nonsingular points of .
Usually we denote by the ring of weakly holomorphic functions through . Since any neighbourhood of a point in is a local analytic subvariety, we can define germs of weakly holomorphic functions at in the obvious way. We usually denote by the ring of germs at of weakly holomorphic functions.
- 1 Hassler Whitney. . Addison-Wesley, Philippines, 1972.
|Date of creation||2013-03-22 17:41:46|
|Last modified on||2013-03-22 17:41:46|
|Last modified by||jirka (4157)|