Computable Real‐Valued Functions on Recursive Open and Closed Subsets of Euclidean Space
Copyright policy )Computable Real‐Valued Functions on Recursive Open and Closed Subsets of Euclidean Space
AbstractIn this paper we study intrinsic notions of “computability” for open and closed subsets of Euclidean space. Here we combine together the two concepts, computability on abstract metric spaces and computability for continuous functions, and delineate the basic properties of computable open and closed sets. The paper concludes with a comprehensive examination of the Effective Riemann Mapping Theorem and related questions.
- Zhongshan Hospital of Xiamen University China (People's Republic of)
- Sun Yat-sen University China (People's Republic of)
- University of Minnesota Morris United States
conformal mapping, Applications of computability and recursion theory, computable open and closed subsets of closed rectangles of Euclidean space, recursive analysis, Euclidean geometries (general) and generalizations, Riemann Mapping Theorem, Tietze Extension Theorem, Constructive and recursive analysis, Inverse Function Theorem
conformal mapping, Applications of computability and recursion theory, computable open and closed subsets of closed rectangles of Euclidean space, recursive analysis, Euclidean geometries (general) and generalizations, Riemann Mapping Theorem, Tietze Extension Theorem, Constructive and recursive analysis, Inverse Function Theorem
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