A pair , where is an arcwise-connected Hausdorff space and is a local homeomorphism, called a projection. Covering domains are encountered in the analytic continuation of holomorphic functions. For every analytic (possibly multivalent) function in a domain there is a corresponding covering domain with a projection , just as for every analytic function of one complex variable there is a corresponding Riemann surface; the function is single-valued on . Covering domains are also called Riemann domains.
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|[a1]||R.C. Gunning, H. Rossi, "Analytic functions of several complex variables" , Prentice-Hall (1965) pp. Chapt. 1, Section G|
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Covering domain. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Covering_domain&oldid=14568