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Inspired by the Pour-El and Richards equivalence theorem between computability and boundedness for closed linear operators on Banach spaces, we study the rather general situation of partial homomorphisms between metric partial universal algebras. First, we develop a set of basic notions and results that reveal some of the delicate algebraic, topological and effective properties of partial algebras. Our main computability concepts are based on numerations and include those of effective metric partial algebras and effective partial homomorphisms. We prove a general equivalence theorem that includes a version of the Pour-El and Richards Theorem, and has other applications. Finally, the Pour-El and Richards axioms for computable sequence structures on Banach spaces are generalised to computable partial sequence structures on metric algebras, and we prove their equivalence with our computability model based on numerations.<\/jats:p>","DOI":"10.2178\/bsl\/1058448675","type":"journal-article","created":{"date-parts":[[2005,3,2]],"date-time":"2005-03-02T20:38:49Z","timestamp":1109795929000},"page":"299-334","source":"Crossref","is-referenced-by-count":15,"title":["Computable and Continuous Partial Homomorphisms on Metric Partial Algebras"],"prefix":"10.1017","volume":"9","author":[{"given":"Viggo","family":"Stoltenberg-Hansen","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"John V.","family":"Tucker","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,1,15]]},"reference":[{"key":"S1079898600004406_ref030","first-page":"40","article-title":"Notation systems and recursive ordered fields","volume":"17","author":"Moschovakis","year":"1966","journal-title":"Composito Mathematica"},{"key":"S1079898600004406_ref025","first-page":"2478","article-title":"Extension de la notion de fonction r\u00e9cursive aux fonctions d'une ou plusieurs variables r\u00e9elles I, II, III","volume":"240","author":"Lacombe","year":"1955","journal-title":"Comptes Rendus de l'Acad\u00e9mie des Sciences"},{"key":"S1079898600004406_ref040","doi-asserted-by":"publisher","DOI":"10.1016\/S0049-237X(99)80028-7"},{"key":"S1079898600004406_ref054","doi-asserted-by":"publisher","DOI":"10.1112\/S0024611502013643"},{"key":"S1079898600004406_ref047","first-page":"1","article-title":"Computability and Frechet spaces","volume":"42","author":"Washihara","year":"1995","journal-title":"Mathematica Japonica"},{"key":"S1079898600004406_ref023","first-page":"101","volume-title":"Constructivity in mathematics","author":"Kreisel","year":"1959"},{"key":"S1079898600004406_ref015","first-page":"37","volume-title":"Constructivity in mathematics","author":"Goodstein","year":"1959"},{"key":"S1079898600004406_ref011","doi-asserted-by":"publisher","DOI":"10.1002\/malq.19730191901"},{"key":"S1079898600004406_ref055","doi-asserted-by":"publisher","DOI":"10.1016\/S0304-3975(98)00301-6"},{"key":"S1079898600004406_ref024","volume-title":"Translations of mathematical monographs","volume":"60","author":"Kushner","year":"1984"},{"key":"S1079898600004406_ref052","first-page":"697","volume-title":"Automata, languages and programming, 26th colloquium, 1999","volume":"1644","author":"Weihrauch","year":"1999"},{"key":"S1079898600004406_ref045","first-page":"230","article-title":"On computable numbers, with an application to the entscheidungsproblem","volume":"42","author":"Turing","year":"1936","journal-title":"Proceedings of the London Mathematical Society"},{"key":"S1079898600004406_ref020","volume-title":"Introduction to topological groups","author":"Husain","year":"1966"},{"key":"S1079898600004406_ref010","doi-asserted-by":"publisher","DOI":"10.1007\/BF02219096"},{"key":"S1079898600004406_ref017","doi-asserted-by":"crossref","first-page":"168","DOI":"10.4064\/fm-42-1-168-202","article-title":"Computable functionals","volume":"42","author":"Grzegorczyk","year":"1955","journal-title":"Fundamenta Mathematicae"},{"key":"S1079898600004406_ref044","unstructured":"Tucker J. 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