Related papers: Representations of Domains via CF-approximation Sp…

Domain theory has its origins in Mathematics and Theoretical Computer Science. Mathematically it combines order and topology. Its central concepts have their origin in the idea of approximating ideal objects by their relatively finite or,…

Web spaces, wide web spaces and worldwide web spaces (alias C-spaces) provide useful generalizations of continuous domains. We present new characterizations of such spaces and their patch spaces, obtained by joining the original topology…

In this paper we determine the representation type of some algebras of infinite matrices continuously controlled at infinity by a compact metrizable space. We explicitly classify their finitely presented modules in the finite and tame…

The main result of this paper may be stated as a construction of "almost representations" for the canonical presheaves of object extensions of length n on the C-systems defined by locally cartesian closed universe categories with binary…

The residual finite-dimensionality of a $\mathrm{C}^*$-algebra is known to be encoded in a topological property of its space of representations, stating that finite-dimensional representations should be dense therein. We extend this…

Automatic presentations, also called FA-presentations, were introduced to extend finite model theory to infinite structures whilst retaining the solubility of fundamental decision problems. A particular focus of research has been the…

Representation stability is a theory describing a way in which a sequence of representations of different groups is related, and essentially contains a finite amount of information. Starting with Church-Ellenberg-Farb's theory of…

When the semantics of a sentence are not representable in a semantic parser's output schema, parsing will inevitably fail. Detection of these instances is commonly treated as an out-of-domain classification problem. However, there is also a…

The paper is concerned with `geometrization' of smooth (i.e. with open stabilizers) representations of the automorphism group of universal domains, and with the properties of `geometric' representations of such groups. As an application, we…

We propose a generalization of continuous lattices and domains through the concept of enriched closure space, defined as a closure space equipped with a preclosure operator satisfying some compatibility conditions. In this framework we are…

The strong shape category of compact metrizable spaces (compacta) is very well-studied; extending it to noncompact spaces, however, introduces computational complexity that makes it hard to work with. The fine shape category, as defined by…

We use model theoretic techniques to construct explicit first-order axiomatizations for the classes of posets that can be represented as systems of sets, where the order relation is given by inclusion, and existing meets and joins of…

Approximation Fixpoint Theory (AFT) is an algebraic framework designed to study the semantics of non-monotonic logics. Despite its success, AFT is not readily applicable to higher-order definitions. To solve such an issue, we devise a…

We explain how the notion of homotopy colimits gives rise to that of mapping spaces, even in categories which are not simplicial. We apply the technique of model approximations and use elementary properties of the category of spaces to be…

The article covers developments in the representation theory of finite group schemes over the last fifteen years. We start with the finite generation of cohomology of a finite group scheme and proceed to discuss various consequences and…

In the present paper a new concept of representability is introduced, which can be applied to not total and also to intransitive relations (semiorders in particular). This idea tries to represent the orderings in the simplest manner,…

In this article, we introduce a new family of sense preserving harmonic mappings f in the open unit disk and prove that functions in this family are close-to-convex. We give some basic properties such as coefficient bounds, growth…

We develop domain theory in constructive univalent foundations without Voevodsky's resizing axioms. In previous work in this direction, we constructed the Scott model of PCF and proved its computational adequacy, based on directed complete…

For a given poset, we consider its representations by systems of subspaces of a unitary space ordered by inclusion. We classify such systems for all posets for which an explicit classification is possible.

Tree sets are abstract structures that can be used to model various tree-shaped objects in combinatorics. Finite tree sets can be represented by finite graph-theoretical trees. We extend this representation theory to infinite tree sets.…