Some subring properties of the ring of holomorphic functions on a non - empty subset of an open Riemann surface

Authors : N İSPİR

Pages : 0-0

Doi:10.1501/Commua1_0000000528

View : 13 | Download : 12

Publication Date : 1990-01-01

Article Type : Research Paper

Abstract :Throughout this paper R and S will denote öpen Riemann surfa- ces and X, Y will be non-empty subsets of R and S, respectively. A func- tion 0 : X -> S is said to be analytic if for each point p e X there is an öpen neighborhood Up of p and an analytic function ıpp : Up S such that 4>p and 0 coincide on Up p X. This is eguivalent to assuming that there is a single öpen set Ü a X and an analytic function 0 : U —> S such th at ıp | X = 0.L et Ainsert ignore into journalissuearticles values(X,Y); denote the set of ali analytic functions 0 : X S with 0insert ignore into journalissuearticles values(X ); c Y. For Y = S = C , a functionin Ainsert ignore into journalissuearticles values(X, C); is called holomorphic and we write Hinsert ignore into journalissuearticles values(X); = Ainsert ignore into journalissuearticles values(X,C);.
Keywords : properties, functions, Riemann