nLab
complex n-dimensional space

Given a positive integer nn, the complex nn-dimensional space n\mathbb{C}^n is the set of nn-tuples of complex numbers considered as a nn-dimensional topological vector over the field of complex numbers \mathbb{C} (such a Hausdorff topology is unique). For a continuous map from a complex nn-dimensional space to a complex mm-dimensional space this structure is enough to define complex differentiability of a map, hence the complex analytic structure is induced.

Created on August 7, 2016 at 10:50:38. See the history of this page for a list of all contributions to it.