Related papers: Order isomorphisms between bases of topologies

We make several new contributions to the study of proper holomorphic mappings between balls. Our results include a degree estimate for rational proper maps, a new gap phenomenon for convex families of arbitrary proper maps, and an…

In this paper, the authors mainly discuss the images of spaces with an uniform base at non-isolated points, and obtain the following main results: (1)\ Perfect maps preserve spaces with an uniform base at non-isolated points; (2)\ Open and…

We study holomorphic isometries between bounded symmetric domains with respect to the Bergman metrics up to a normalizing constant. In particular, we first consider a holomorphic isometry from the complex unit ball into an irreducible…

We survey the theory of totally symmetric sets, with applications to homomorphisms of symmetric groups, braid groups, linear groups, and mapping class groups.

The concept of quasi-isometric embedding maps between $*$-algebras is introduced. We have obtained some basic results related to this notion and similar to quasi-isometric embedding maps on metric spaces, under some conditions, we give a…

We study the maps between topological spaces whose composition with Baire class $\alpha$ maps also belongs to the $\alpha$'th Baire class and give characterizations of such maps

A new and extensive formalism is developed for monads and galaxies in non-standard enlargements. It is shown that monads and galaxies can be manipulated using order-preserving and order-reversing set-to-set maps, and that set properties…

This paper is a continuation of the papers [2,3,4,5,6]. In this paper the osculating spaces of arbitrary order of a manifold embedded in Euclidean space are considered. A better estimation of their dimensions as well as the description of…

We elaborate an algebraic framework for describing internal topological symmetries of gapped boundaries of (2+1)D topological orders. We present a categorical obstruction to the coherence of bulk group symmetry and boundary symmetries in…

The Modular Isomorphism Problem asks, if an isomorphism between modular group algebras of finite $p$-groups over a field $F$ implies an isomorphism of the group bases. We explore the differences of knowledge on the problem when $F$ is…

This paper presents a new version of boundary on coarse spaces. The space of ends functor maps coarse metric spaces to uniform topological spaces and coarse maps to uniformly continuous maps.

We show that a topometric space $X$ is topometrically isomorphic to a type space of some continuous first-order theory if and only if $X$ is compact and has an open metric (i.e., satisfies that $\{p : d(p,U) < \varepsilon\}$ is open for…

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 construct a family of separable Hilbertian operator spaces, such that the relation of complete isomorphism between the subspaces of each member of this family is complete $\ks$. We also investigate some interesting properties of…

Theory of representations of F-algebra is a natural development of the theory of F-algebra. Exploring of morphisms of the representation leads to the concepts of generating set and basis of representation. In the book I considered the…

In architecture, city planning, visual arts, and other design areas, shapes are often made with points, or with structural representations based on point-sets. Shapes made with points can be understood more generally as finite arrangements…

We establish a bijection between the set of finite topological $T_0$-spaces (or partially ordered sets) and equivalence classes of square matrices. The absolute value of the determinant or the rank of these matrices serve as simple homotopy…

This is the third revision. We study bases of Pfaffian systems for $A$-hypergeometric system. Gr\"obner deformations give bases. These bases also give those for twisted cohomology groups. For hypergeometric system associated to a class of…

We define a moduli space of translation structures on the open topological disk with a basepoint and endow it with a locally-compact metrizable topology. We call this the immersive topology, because it is defined using the concept of…

Partially ordered sets (posets) play a universal role as an abstract structure in many areas of mathematics. For finite posets, an explicit enumeration of distinct partial orders on a set of unlabelled elements is known only up to a…