Notions of semicomputability in topological algebras over the reals

Several results from classical computability theory (computability over discrete structures such as the natural numbers and strings over finite alphabets, due to Turing, Church, Kleene and others) have been shown to hold for generalisations of computability theory over total abstract algebras, using a computation model of a high level imperative (While) language. We present a number of results relating to computation on topological partial …