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RECURSIVE BAIRE CLASSIFICATION AND SPEEDABLE FUNCTIONS

Cristian S. Calude, Gabriel Istrate, Marius Zimand

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Abstract

Abstract Using recursive variants of Baire notions of nowhere dense and meagre sets we study the topological size of speedable and infinitely often speedable functions in a machine‐independent framework. We show that the set of speedable functions is not “small” whereas the set of infinitely often speedable functions is “large”. In this way we offer partial answers to a question in [4].

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What this paper is about

Abstract Using recursive variants of Baire notions of nowhere dense and meagre sets we study the topological size of speedable and infinitely often speedable functions in a machine‐independent framework. We show that the set of speedable functions is not “small” whereas the set of infinitely often speedable functions is “large”. In this way we offer partial answers to a question in [4].

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Available abstract

Abstract Using recursive variants of Baire notions of nowhere dense and meagre sets we study the topological size of speedable and infinitely often speedable functions in a machine‐independent framework. We show that the set of speedable functions is not “small” whereas the set of infinitely often speedable functions is “large”. In this way we offer partial answers to a question in [4].

Key concepts: Baire category theorem, Baire measure, Baire space, Mathematics, Nowhere dense set, Set (abstract data type), Pure mathematics, Discrete mathematics

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