In this paper we introduce and compare computability concepts on the set of closed subsets of Euclidean space. We use the language and framework of Type 2 Theory of Effectivity (TTE) which supplies a… (More)

The Graph Theorem of classical recursion theory states that a total function on the natural numbers is computable, if and only if its graph is recursive. It is known that this result can be… (More)

The investigation of computational properties of discontinuous functions is an important concern in computable analysis. One method to deal with this subject is to consider effective variants of… (More)

The notions “recursively enumerable” and “recursive” are the basic notions of e-ectivity in classical recursion theory. In computable analysis, these notions are generalized to closed subsets of… (More)

In this paper we study a new approach to classify mathematical theorems according to their computational content. Basically, we are asking the question which theorems can be continuously or… (More)

We characterize some major algorithmic randomness notions via differentiability of effective functions. (1) As the main result we show that a real number z ∈ [0, 1] is computably random if and only… (More)

In this paper we study a reducibility that has been introduced by Klaus Weihrauch or, more precisely, a natural extension of this reducibility for multi-valued functions on represented spaces. We… (More)

A metric defined by Fine induces a topology on the unit interval which is strictly stronger than the ordinary Euclidean topology and which has some interesting applications in Walsh analysis. We… (More)

We classify the computational content of the Bolzano-Weierstraß Theorem and variants thereof in the Weihrauch lattice. For this purpose we first introduce the concept of a derivative or jump in this… (More)