相关论文: Between ${\cal A}$- and ${\cal B}$-sets
In real-world scenarios classification models are often required to perform robustly when predicting samples belonging to classes that have not appeared during its training stage. Open Set Recognition addresses this issue by devising models…
We show that any translate of a model set is a model set in some modified cut-and-project scheme. Restricting to Euclidean direct space, we show that any translate of an inter model set is a model set in some modified cut-and-project scheme…
The goal of this short note is to prove that when $A$ is a closed *-subalgebra of a C*-algebra $B$ satisfying the ideal intersection property plus a mild axiom (INV), then the map $J\mapsto J\cap A$ establishes an isomorphism from the…
Soft sets, as a mathematical tool for dealing with uncertainty, have recently gained considerable attention, including some successful applications in information processing, decision, demand analysis, and forecasting. To construct new soft…
A linear-interval order is the intersection of a linear order and an interval order. For this class of orders, several structural results have been known. This paper introduces a new subclass of linear-interval orders. We call a partial…
In [S. Basu, A. Gabrielov, N. Vorobjov, Semi-monotone sets. arXiv:1004.5047v2 (2011)] we defined semi-monotone sets, as open bounded sets, definable in an o-minimal structure over the reals, and having connected intersections with all…
The purpose of this book is to lay out certain aspects of descriptive set theory. After initially establishing notation and generalities we proceed to the following topics: partitions, semirings, rings, $\sigma$-rings, $\delta$-rings,…
Integral categories form a sub-class of pre-abelian categories whose systematic study was initiated by Rump in 2001. In the first part of this article we determine whether several categories of topological and bornological vector spaces are…
A ballean $\mathcal{B}$ (or a coarse structure) on a set $X$ is a family of subsets of $X$ called balls (or entourages of the diagonal in $X\times X$) defined in such a way that $\mathcal{B}$ can be considered as the asymptotic counterpart…
The notion of preopen sets and precontinuity in a topological space was introduced by Mashhour et. al in 1982 [13]. Later the same was studied in a bitopological space in [7] and [9]. Here we have studied the idea of pairwise preopen sets…
In this paper, we have established boundaries of cardinal numbers of nonempty sets in finite non-$T_1$ topological spaces using interval analysis. For a finite set with known cardinality, we give interval estimations based on the closure…
The article is devoted to a structure of topological spaces related with topological quasigroups. Regular and complete spaces over topological quasigroups are studied. Separations and embeddings are also investigated for them. Their…
We prove a categorical duality between a class of abstract algebras of partial functions and a class of (small) topological categories. The algebras are the isomorphs of collections of partial functions closed under the operations of…
We have studied the concept of bipolarity of information in the soft sets. We have defined bipolar soft sets and basic operations of union, intersection and complementation for bipolar soft sets. Examples of bipolar soft sets and an…
In this paper, the author introduce and study the notion of pre-{\gamma}-I-open sets in ideal topological space.
A description of all subsemigroups of $M_2(\mathbb{C})$ which are given by a countable intersection of constructible sets is given. Furthermore, it is shown that they are intersections of constructible semigroups.
In this paper, we introduce and study two new classes of commutative rings, namely semi transitional rings and transitional rings, which extend several classical ideas arising from rings of continuous functions and their variants. A general…
The goal of this article is to emphasize the role of cubical sets in enriched categories theory and infinity-categories theory. We show in particular that categories enriched in cubical sets provide a convenient way to describe many…
We give a self-contained introduction to accessible categories and how they shed light on both model- and set-theoretic questions. We survey for example recent developments on the study of presentability ranks, a notion of cardinality…
The binomial interpolated transform of a sequence is a generalization of the well-known binomial transform. We examine a Pascal-like triangle, on which a binomial interpolated transform works between the left and right diagonals, focusing…