Index sets in computable analysis
Pi(1)(0) classes in a space X where X equals {0, 1}(omega), omega(omega), [0,1], or the real line R are given an effective enumeration P(e,x) and the computably continuous functions are given an effective enumeration F(e,x). The notion of index sets associated with Pi(1)(0) classes and with computably continuous functions is developed. The complexity of various problems of analysis is determined by the complexity of the associated index set. (C) 1999 Elsevier Science B.V. All rights reserved.
index set computable analysis pi-0-1 class