相关论文: A (co)homology theory for some preordered topologi…
In this paper, we investigate the notion of partition of a finite partially ordered set (poset, for short). We will define three different notions of partition of a poset, namely, monotone, regular, and open partition. For each of these…
In order theory, partially ordered sets are only equipped with one relation which decides the entire structure/Hasse diagram of the set. In this paper, we have presented how partially ordered sets can be studied under simultaneous partially…
A plane poset is a finite set with two partial orders, satisfying a certain incompatibility condition. The set PP of isoclasses of plane posets owns two products, and an infinitesimal Hopf algebra structure is defined on the vector space…
These lecture notes for the IAS/Park City Graduate Summer School in Geometric Combinatorics (July 2004) provide an overview of poset topology. These notes include introductory material, as well as recent developments and open problems. Some…
Earlier an arbitrary poset $P$ was proved to be isomorphic to the collection of subsets of a space $M$ with two closures which are closed in the first closure and open in the other. As a space $M$ for this representation an algebraic dual…
In this paper we have shown that a double sequence in a topological space satisfies certain conditions which in turn are capable to generate a topology on a non empty set. Also we have used the idea of I-convergence of double sequences to…
We define toric partial orders, corresponding to regions of graphic toric hyperplane arrangements, just as ordinary partial orders correspond to regions of graphic hyperplane arrangements. Combinatorially, toric posets correspond to finite…
This note is a survey on the topology of hyperplane arrangements. We mainly focus on the relationship between topology and the real structure, such as adjacent relations of chambers and stratifications related to real structures.
We introduce decomposition complexes of posets, which generalize order complexes. The main advantage of our construction is that decomposition complexes are closed under taking products. Other special instances of this theory include nested…
The aim of this paper is to study co-prolongations of central extensions. We construct the obstruction theory for co-prolongations and classify the equivalence classes of these by kernels of a homomorphisms between 2-dimensional cohomology…
We compute the cohomology ring of a generalised type of configuration space of points in $\mathbb{R}^r$. This configuration space is indexed by a graph. In the case the graph is complete the result is known and it is due to Arnold and…
We introduce a version of discrete Morse theory for posets. This theory studies the topology of the order complexes K(X) of h-regular posets X from the critical points of admissible matchings on X. Our approach is related to R. Forman's…
Covering-based rough set theory is an extension to classical rough set. The main purpose of this paper is to study covering rough sets from a topological point of view. The relationship among upper approximations based on topological spaces…
We study the homotopy theory of locally ordered spaces, that is manifolds with boundary whose charts are partially ordered in a compatible way. Their category is not particularly well-behaved with respect to colimits. However, this category…
A quotient of a poset $P$ is a partial order obtained on the equivalence classes of an equivalence relation $\theta$ on $P$; $\theta$ is then called a congruence if it satisfies certain conditions, which vary according to different…
Let $\mathfrak{P}$ be a topological property. We study the relation between the order structure of the set of all $\mathfrak{P}$-extensions of a completely regular space $X$ with compact remainder (partially ordered by the standard partial…
A co-valuation is, essentially, a minimal finite cover. We introduce a logic based on co-valuations, which play the role of valuations of free variables in classical first-order logic, and show that the fundamental tools of model theory --…
A toric arrangement is an arrangement of subtori of codimension one in a real or complex torus. The poset of layers is the set of connected components of non-empty intersections of these subtori, partially ordered by reverse inclusion. In…
We define a homology theory for a certain class of posets equipped with a representation. We show that when restricted to Boolean lattices this homology is isomorphic to the homology of the "cube" complex defined by Khovanov.
The intrinsic connection between lattice theory and topology is fairly well established, For instance, the collection of open subsets of a topological subspace always forms a distributive lattice. Persistent homology has been one of the…