Related papers: Precompact Apartness Spaces

In this paper, we deal with uniform spaces whose diagonal uniformity admits a basis consisting of equivalence relations. Such non-Archimedean uniform spaces are particularly interesting for applications in commutative ring theory, because…

We introduce a notion of a filtered model structure and use this notion to produce various model structures on pro-categories. This framework generalizes several known examples. We give several examples, including a homotopy theory for…

We discuss supernear spaces.

Learning Spaces are certain set systems that are applied in the mathematical modeling of education. We propose a suitable compression (without loss of information) of such set systems to facilitate their logical and statistical analysis.…

In this note we study some properties of topological entropy for noncompact non-metrizable spaces.

The compactness theorem for a logic states, roughly, that the satisfiability of a set of well-formed formulas can be determined from the satisfiability of its finite subsets, and vice versa. Usually, proofs of this theorem depend on the…

Constructive properties of uniform convexity, strict convexity, near convexity, and metric convexity in real normed linear spaces are considered. Examples show that certain classical theorems, such as the existence of points of osculation,…

What does it mean for an algorithm to be fair? Different papers use different notions of algorithmic fairness, and although these appear internally consistent, they also seem mutually incompatible. We present a mathematical setting in which…

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.

We analyze the embedding properties between Besov spaces, defined on the total space $\mathbb R^n$ and on bounded domains. We give a complete classification on whether or not these embedding maps satisfy certain weak compactness…

We introduce a new covering property, defined in terms of order types of sequences of open sets, rather than in terms of cardinalities of families. The most general form of this compactness notion depends on two ordinal parameters. In the…

The purpose of this note is to introduce primitive ideals of noncommutative semigroups and study some topological aspects of the corresponding structure spaces.

We introduce a topology on the space of all isomorphism types represented in a given class of countable models, and use this topology as an aid in classifying the isomorphism types. This mixes ideas from effective descriptive set theory and…

The purpose of this note is to illustrate a parallel between (pre)topologies when seen among convergence spaces and (pre)approach spaces when seen among convergence approach spaces, that appears to be a more complete parallel than in the…

The compactness phenomenon is one of the featured aspects of structuralism in mathematics. In simple and broad words, a compactness property holds in a structure if a related property is satisfied by sufficiently many substructures of that…

This paper gives a uniform-theoretic refinement of classical homotopy theory. Both cubical sets (with connections) and uniform spaces admit classes of weak equivalences, special cases of classical weak equivalences, appropriate for the…

We characterize ultrafilter convergence and ultrafilter compactness in linearly ordered and generalized ordered topological spaces. In such spaces, and for every ultrafilter $D$, the notions of $D$-compactness and of $D$-pseudocompactness…

We define a class of subsets of a topological space that coincides with the class of compact saturated subsets when the space is sober, and with enough good properties when the space is not sober. This class is introduced especially in view…

In this paper we introduce a new kind of topological space, called 'structured space', which locally resembles various kinds of algebraic structures. This can be useful, for instance, to locally study a space that cannot be globally endowed…

We provide a model theoretical and tree property like characterization of $\lambda$-$\Pi^1_1$-subcompactness and supercompactness. We explore the behaviour of those combinatorial principles at accessible cardinals.