## 67 Citations

### Computability over Topological Structures

- Mathematics
- 2003

Computable analysis is the Turing machine based theory of computability on the real numbers and other topological spaces. Similarly as Ersov’s concept of numberings can be used to deal with discrete…

### A Foundation for Computable Analysis

- Mathematics, Computer ScienceSOFSEM
- 1997

The paper gives a short introduction to basic concepts of TTE (Type 2 Theorie of Effectivity), and shows its general applicability by some selected examples, and discusses the problem of zero-finding.

### Computable Analysis: An Introduction

- EducationTexts in Theoretical Computer Science. An EATCS Series
- 2000

This book provides a solid fundament for studying various aspects of computability and complexity in analysis and is written in a style suitable for graduate-level and senior students in computer science and mathematics.

### Notions of computability at higher types I

- Mathematics
- 2016

An extended survey of the different strands of research on higher type computability to date is given, bringing together material from recursion theory, constructive logic and computer science.

### On the topological aspects of the theory of represented spaces

- MathematicsComput.
- 2016

This work presents an abstract and very succinct introduction to the theory of represented spaces, drawing heavily on prior work by Escardo, Schroder, and others.

### Recursion and topology on 2 6 ! for possibly in ' nite computations Ver )

- Mathematics
- 2004

In the context of possibly in'nite computations yielding 'nite or in'nite (binary) outputs, the space 2 = 2∗ ∪ 2 appears to be one of the most fundamental spaces in Computer Science. Though…

### Computability on Subsets of Euclidean Space I: Closed and Compact Subsets

- Mathematics, Computer ScienceTheor. Comput. Sci.
- 1999

### Recursion and Topology on 2 ≤ ω for Possibly Infinite Computations

- Computer Science, Mathematics
- 2006

For (semi)continuous and (semia)computable maps F : I → O with I,O ∈ {2ω, 2≤ω} a detailed representation theorem is proved via functions f : 2∗ → 2∪2ω following two approaches: bottom-up from f to F and top-down from F to f .

## References

SHOWING 1-10 OF 15 REFERENCES

### The hereditary partial effective functionals and recursion theory in higher types

- Mathematics, Computer ScienceJournal of Symbolic Logic
- 1984

Abstract A type-structure of partial effective functionals over the natural numbers, based on a canonical enumeration of the partial recursive functions, is developed. These partial functionals,…

### Computability concepts for programming language semantics

- Computer ScienceTheor. Comput. Sci.
- 1976

A notion of computability on continuous higher types (for all types) is defined and its equivalence to effective operators is shown and shows that the authors' computable operators can model mathematically everything that can be done in an operational semantics.

### A Machine-Independent Theory of the Complexity of Recursive Functions

- Computer ScienceJACM
- 1967

The number of steps required to compute a function depends on the type of computer that is used, on the choice of computer program, and on the input-output code, but the results obtained in this paper are nearly independent of these considerations.

### Recursion theoretic operators and morphisms of numbered sets

- Mathematics
- 1983

An operator is a map <P\ Pto —» Poj. By embedding Pto in two natural ways into the A-calculus model Pto2 (and T°) the computable maps on this latter structure induce classes of recursion operators. §…

### Theory of Recursive Functions and Effective Computability

- Computer Science
- 1969

Central concerns of the book are related theories of recursively enumerable sets, of degree of un-solvability and turing degrees in particular and generalizations of recursion theory.

### Data Types as Lattices

- MathematicsSIAM J. Comput.
- 1976

The meaning of many kinds of expressions in programming languages can be taken as elements of certain spaces of “partial” objects. In this report these spaces are modeled in one universal domain…

### Some Ordered Sets in Computer Science

- Mathematics
- 1982

For the most part in the lectures the authors shall concentrate on the finitary domains, but the continuous domains find an interest as a generalization of interval analysis and by the connection with spaces of upper-semicontinuous functions.