I present a basic result about Cantor space in the context of com-putability theory: the computable Cantor space is computably non-compact. This is in sharp contrast with the classical theorem that Cantor space is compact. The note is written for mathematicians with classical training in topology and analysis. I assume nothing from computability theory, except the basic intuition about how computers work by executing in-structions given by a finite program.
The Cantor Set is a famous topological set developed from an infinite process of starting with the i...
This research is about operational- and complexity-oriented aspects of classical foundations of com-...
AbstractIn the context of possibly infinite computations yielding finite or infinite (binary) output...
New constructive definition of compactness in the form of the existence of a continuous ”uni-versal ...
In the context of possibly infinite computations yielding finite or infinite (binary) outputs, the s...
The topic is layerwise computability. n In which field is the notion used?- (mainly) Computable Anal...
Abstract The space of one-sided infinite words plays a crucial rôle in several parts of Theoretical ...
We revise and extend the foundation of computable topology in the framework of Type-2 theory of effe...
AbstractWe consider an abstract metric space with a computability structure and an effective separat...
Computability and continuity are closely linked - in fact, continuity can be seen as computability r...
summary:A.V. Arkhangel'skii asked that, is it true that every space $Y$ of countable tightness is ho...
Abstract Stone Duality is a re-axiomatisation of general topology in which the topology on a space i...
A compact set has computable type if any homeomorphic copy of the set which is semicomputable is act...
We investigate structures of size at most continuum using various techniques originating from comput...
We continue the investigation of analytic spaces from the perspective of computable structure theory...
The Cantor Set is a famous topological set developed from an infinite process of starting with the i...
This research is about operational- and complexity-oriented aspects of classical foundations of com-...
AbstractIn the context of possibly infinite computations yielding finite or infinite (binary) output...
New constructive definition of compactness in the form of the existence of a continuous ”uni-versal ...
In the context of possibly infinite computations yielding finite or infinite (binary) outputs, the s...
The topic is layerwise computability. n In which field is the notion used?- (mainly) Computable Anal...
Abstract The space of one-sided infinite words plays a crucial rôle in several parts of Theoretical ...
We revise and extend the foundation of computable topology in the framework of Type-2 theory of effe...
AbstractWe consider an abstract metric space with a computability structure and an effective separat...
Computability and continuity are closely linked - in fact, continuity can be seen as computability r...
summary:A.V. Arkhangel'skii asked that, is it true that every space $Y$ of countable tightness is ho...
Abstract Stone Duality is a re-axiomatisation of general topology in which the topology on a space i...
A compact set has computable type if any homeomorphic copy of the set which is semicomputable is act...
We investigate structures of size at most continuum using various techniques originating from comput...
We continue the investigation of analytic spaces from the perspective of computable structure theory...
The Cantor Set is a famous topological set developed from an infinite process of starting with the i...
This research is about operational- and complexity-oriented aspects of classical foundations of com-...
AbstractIn the context of possibly infinite computations yielding finite or infinite (binary) output...