Related papers: Computably Based Locally Compact Spaces
Under a general categorical procedure for the extension of dual equivalences as presented in this paper's predecessor, a new algebraically defined category is established that is dually equivalent to the category $\bf LKHaus$ of locally…
This book provides an introduction to the theory of digital (molecular) spaces (TDS). Digital spaces are combinatorial models of continuous spaces. TDS is one of alternative branches of digital topology that studies constructing and…
The notion of soft sets is introduced as a general mathematical tool for dealing with uncertainty. In this paper, we consider the concepts of soft compactness, countably soft compactness and obtain some results. We study some soft…
Motivated by a recent result of Prasad, we consider three stronger notions of arithmetic equivalence: local integral equivalence, integral equivalence, and solvable equivalence. In addition to having the same Dedekind zeta function (the…
Stone locales together with continuous maps form a coreflective subcategory of spectral locales and perfect maps. A proof in the internal language of an elementary topos was previously given by the second-named author. This proof can be…
An asymptotically AdS geometry connecting two or more boundaries is given by a entangled state, that can be expanded in the product basis of the Hilbert spaces of each CFT living on the boundaries. We derive a prescription to compute this…
In this paper we consider a class of static spacetimes in higher dimensional ($D \ge 4$) scalar-torsion theories with non-minimal derivative coupling and the scalar potential turned on. The spacetime is conformal to a product space of a…
We integrate $\Lambda_{\rm s}$CDM, a promising scenario for alleviating cosmological tensions, into VCDM, a type-II minimally modified gravity. This promotes the scenario to a fully predictive model (dubbed $\Lambda_{\rm s}$VCDM) that…
This work develops a multiscale solution decomposition (MSD) method for nonlocal-in-time problems to separate a series of known terms with multiscale singularity from the original singular solution such that the remaining unknown part…
We explore some of the global aspects of duality transformations in String Theory and Field Theory. We analyze in some detail the equivalence of dual models corresponding to different topologies at the level of the partition function and in…
Definition of the partition function of U(1) gauge theory is extended to a class of four-manifolds containing all compact spaces and certain asymptotically locally flat (ALF) ones including the multi-Taub--NUT spaces. The partition function…
Recently there have been discussions about which complex metrics should be allowable in quantum gravity. These discussions assumed that the matter fields were real valued. We make the observation that for compactified solutions it makes…
We already saw in [A1] that the space of dynamically marked rational maps can be identified to a subspace of the space of covers between trees of spheres on which there is a notion of convergence that makes it sequentially compact. In the…
In [1] we introduced the concept of structured space, which is a topological space that locally resembles some algebraic structures. In [2] we proceeded the study of these spaces, developing two cohomology theories. The aim of this paper is…
Let $S$ be an integral domain with field of fractions $F$ and let $A$ be an $F$-algebra. An $S$-subalgebra $R$ of $A$ is called $S$-nice if $R$ is lying over $S$ and the localization of $R$ with respect to $S \setminus \{ 0 \}$ is $A$. Let…
Cluster varieties are geometric objects that have recently found applications in several areas of mathematics and mathematical physics. This thesis studies the geometry of a large class of cluster varieties associated to compact oriented…
The main goal of this paper is to investigate strong duality of non-convex semidefinite programming problems (SDPs). In the optimization community, it is well-known that a convex optimization problem satisfies strong duality if the Slater's…
The paper presents a new set of axioms of digital topology, which are easily understandable for application developers. They define a class of locally finite (LF) topological spaces. An important property of LF spaces satisfying the axioms…
Associated to a symmetric space there is a canonical connection with zero torsion and parallel curvature. This connection acts as a binary operator on the vector space of smooth sections of the tangent bundle, and it is linear with respect…
By de Vries duality, the category of compact Hausdorff spaces is dually equivalent to the category of de Vries algebras. In our recent article, we have extended de Vries duality to completely regular spaces by generalizing de Vries algebras…