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It is an effective variant of F. Hausdorff's concept of resolvable sets, and it modifies and generalizes notions of recursivity known from computable analysis, formerly used for open or closed sets only, to more general types of sets. Approximate decidability of sets can equivalently be expressed by computability of the characteristic functions by means of appropriately working oracle Turing machines. The notion fulfills some natural requirements and is hereditary under canonical embeddings of sets into spaces of higher dimensions. However, it is not closed under binary union or intersection of sets. We also show how the framework of resolvability and approximate decidability can be applied to investigate concepts of reducibility for subsets of Euclidean spaces.<\/jats:p>","DOI":"10.1002\/malq.200310003","type":"journal-article","created":{"date-parts":[[2003,1,17]],"date-time":"2003-01-17T16:43:11Z","timestamp":1042821791000},"page":"34-56","source":"Crossref","is-referenced-by-count":9,"title":["Approximate decidability in euclidean spaces"],"prefix":"10.1002","volume":"49","author":[{"given":"Armin","family":"Hemmerling","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2003,1,16]]},"reference":[{"key":"e_1_2_1_2_2","doi-asserted-by":"publisher","DOI":"10.1090\/S0273-0979-1989-15750-9"},{"key":"e_1_2_1_3_2","doi-asserted-by":"crossref","unstructured":"L.Blum F.Cucker M.Shub andS.Smale Complexity and Real Computation (Springer\u2010Verlag New York 1998).","DOI":"10.1007\/978-1-4612-0701-6"},{"key":"e_1_2_1_4_2","unstructured":"V.Brattka The emporer's new recursiveness: The epigraph of the exponential function in two models of computability. 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