Related papers: Separated and prime compactifications

In this paper, we study the properties of closure operators obtained as initial lifts along a reflector, and compactness with respect to them in particular. Applications in the areas of topology, topological groups and topological…

There are several compactification procedures in topology, but there is only one standard discretization, namely, replacing the original topology with the discrete topology. We give a notion of discretization which is dual (in categorical…

A thorough classification of the topologies of compact homogeneous universes is given except for the hyperbolic spaces, and their global degrees of freedom are completely worked out. To obtain compact universes, spatial points are…

We construct a triangulation of a compactification of the Moduli space of a surface with at least one puncture that is closely related to the Deligne-Mumford compactification. Specifically, there is a surjective map from the…

We develop a folding approach to study two-dimensional symmetry-enriched topological (SET) phases with the mirror reflection symmetry. Our folding approach significantly transforms the mirror SETs, such that their properties can be…

Motivated by the principles of the conformal bootstrap, primarily the principle of Locality, simultaneously with the requirement of space-time supersymmetry, we reconsider constructions of compactified superstring models. Starting from…

In this paper we introduce congruence spaces, which are topological spaces that are canonically attached to monoid schemes and that reflect closed topological properties. This leads to satisfactory topological characterizations of closed…

We study quasi-modular pseudometric spaces as asymmetric refinements of modular metric structures. To each such space we associate canonical forward and backward quasi-uniformities and the corresponding directional topologies. We introduce…

In this paper we try to look at the compactification of Teichmuller spaces from a tropical viewpoint. We describe a general construction for the compactification of algebraic varieties, using their amoebas, and we describe the boundary via…

We revisit the known problem whether each compact topology is contained in a maximal compact topology and collect some partial answers to this question. For instance we show that each compact topology is contained in a compact topology in…

We provide a necessary and sufficient condition for the embeddability of a metrizable group into semigroup compactifications associated to uniformly continuous functions. Our result employs a technique used by I. Ben Yaacov, A. Berenstein…

Given a closed Riemannian manifold $(N^{n+1},g)$, $n+1 \geq 3$ we prove the compactness of the space of singular, minimal hypersurfaces in $N$ whose volumes are uniformly bounded from above and the $p$-th Jacobi eigenvalue $\lambda_p$'s are…

Over any partially ordered abelian group whose positive cone is closed in an appropriate sense and has finitely many faces, modules that satisfy a weak finiteness condition admit finite primary decompositions. This conclusion rests on the…

For a topological space $X$ its reflection in a class $\mathsf T$ of topological spaces is a pair $(\mathsf T X,i_X)$ consisting of a space $\mathsf T X\in\mathsf T$ and continuous map $i_X:X\to \mathsf T X$ such that for any continuous map…

We generalize to the relations $(\lambda, \mu) \stackrel{\kappa}{\Rightarrow} (\lambda', \mu')$ and $\alm (\lambda, \mu) \stackrel{\kappa}{\Rightarrow} \alm (\lambda', \mu')$ some results obtained in Parts II and IV. We also present a…

We show that some recent constructions in the literature, named `weak' generalizations, can be systematically treated by passing from 2-categories to categories enriched in the Cartesian monoidal category of Cauchy complete categories.

We introduce a general notion of covering property, of which many classical definitions are particular instances. Notions of closure under various sorts of convergence, or, more generally, under taking kinds of accumulation points, are…

We prove that the space of free boundary CMC surfaces of bounded topology, bounded area and bounded boundary length is compact in the $C^k$ graphical sense away from a finite set of points. This is a CMC version of a result for minimal…

We classify compact 2-connected homogeneous spaces with the same rational cohomology as a product of spheres. This classification relies on spectral sequences, homotopy theory, and representation theory. We then apply this classification to…

We use pointwise Kan extensions to generate new subcategories out of old ones. We investigate the properties of these newly produced categories and give sufficient conditions for their cartesian closedness to hold. Our methods are of…