Related papers: Proper spaces are spectral
A lattice is called well-rounded, if its lattice vectors of minimal length span the ambient space. We show that there are interesting connections between the existence of well-rounded sublattices and coincidence site lattices (CSLs).…
We develop a sequential-topological study of rational points of schemes of finite type over local rings typical in higher dimensional number theory and algebraic geometry. These rings are certain types of multidimensional complete fields…
We introduce a very natural topology on the set of total orderings of monomials of any algebra having a countable basis over a field. This topological space and some notable subspaces are compact. This topological framework allows us to…
In this paper we focus on the integrable Teichm\"uller spaces, subspaces of the universal Teichm\"uller space, and we prove that elements of some of them are continuously differentiable.
We review the basic definition of a stack and apply it to the topological and smooth settings. We then address two subtleties of the theory: the correct definition of a ``stack over a stack'' and the distinction between small stacks (which…
Finite metric spaces arise in many different contexts. Enormous bodies of data, scientific, commercial and others can often be viewed as large metric spaces. It turns out that the metric of graphs reveals a lot of interesting information.…
A set $\Omega \subset \mathbb{R}^d$ is said to be spectral if the space $L^2(\Omega)$ has an orthogonal basis of exponential functions. It is well-known that in many respects, spectral sets "behave like" sets which can tile the space by…
We show that the loop spaces of real projective spaces are topologically approximated by the spaces of rational maps from RP(1) to RP(n). As a byproduct of our constructions we obtain an interpretation of the Kronecker characteristic…
In the past few years, the research on sober spaces and well-filtered spaces has got some breakthrough progress. In this paper, we shall present a brief summarising survey on some of such development. Furthermore, we shall pose and…
The collection of $d \times N$ complex matrices with prescribed column norms and prescribed (nonzero) singular values forms a compact algebraic variety, which we refer to as a frame space. Elements of frame spaces -- i.e., frames -- are…
In this article, we will study prime spectrum of Krasner hyperrings and Zariski topology on them, which play an important role in algebraic geometry. Then some results about the relationship between the topological properties of Spec(R) and…
In this paper we prove that the Ziegler spectra of all serial rings are sober. We then use this proof to give a general framework for computing and understanding Ziegler spectra of uniserial rings up to topological indistinguishability.…
Due to the growing interest in embeddings of space-time in higher-dimensional spaces we consider a specific type of embedding. After proving an inequality between intrinsically defined curvature invariants and the squared mean curvature, we…
In this paper, the new concept of quasi-prime ideal is introduced which at the same time generalizes the `prime ideal' and `primary ideal' notions. Then a natural topology on the set of quasi-prime ideals of a ring is introduced which…
We study the topology of the space of positive scalar curvature metrics on high dimensional spheres and other spin manifolds. Our main result provides elements of infinite order in higher homotopy and homology groups of these spaces, which,…
Radial representations of finitely generated free groups are studied. The associated C*-algebra is located between the reduced and full group C*-algebras and its primitive ideal space is described concretely as a topological space.
We show that the spaces of holomorphic and continuous maps from a smooth complex projective variety to a projective space have the same homology in a range depending on the degree of the maps.
We give an explicit description of cubic rings over a discrete valuation ring, as well as a description of all ideals of such rings.
The aim of this paper is to study the topological properties of algebraic sets with zero divisors. We impose a subbasic topology on the set of proper ideals of a $k$-algebra and this new ``$k$-space'' becomes a generalization of the…
An orthogonality space is a set together with a symmetric and irreflexive binary relation. Any linear space equipped with a reflexive and anisotropic inner product provides an example: the set of one-dimensional subspaces together with the…