Let ℋn be the metric space of all bounded domains in ℂn with the metric equal to the Hausdorff distance between boundaries of domains. We prove that the dimension of the group of automorphisms of domains is an upper semicontinuous function on ℋn. We also provide theorems and examples regarding the change in topological structure of these groups under small perturbation of a domain ℋn.
|Original language||English (US)|
|Number of pages||11|
|Journal||American Journal of Mathematics|
|State||Published - Apr 1 2003|
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