A Computational Model for Metric Spaces

In this paper we present an alternative order-theoretic proof of the Banach fixed point theorem for selfmaps on complete metric spaces which is based on formal balls and, contrary to the case of Edalat and Heckmann [Theoret. Comput. Sci. 193 (1998), 53-73], does not derive from the well-known dcpo fixed point theorem. M.S.C. 2000: 06A06, 54E35, 54H25, 54E50, 68Q55. Key words: metric, ordered set, dcpo, formal ball, computational model.

• Type: Journal
• Year: 1998
• Where: TCS
• Authors: Abbas Edalat, Reinhold Heckmann
• Keywords: Alternative Order-theoretic Proof, Formal Ball, Point Theorem, TCS 1998, Theoretical Computer Science