Related papers: Complete topologized posets and semilattices
There exists a physically well motivated method for approximating manifolds by certain topological spaces with a finite or a countable set of points. These spaces, which are partially ordered sets (posets) have the power to effectively…
Recent results concerning the relation of topology and low-lying fermion modes are summarized.
A new model, in terms of finite bipartite graphs, of the free pseudosemilattice is presented. This will then be used to obtain several results about the variety SPS of all strict pseudosemilattices: (i) an identity basis for SPS is found,…
We study geometric and topological properties of locally compact, geodesically complete spaces with an upper curvature bound. We control the size of singular subsets, discuss homotopical and measure-theoretic stratifications and regularity…
Theoretical investigations of different routes to coherent perfect polarization rotation illustrate its phenomenological connection with coherent perfect absorption. Studying systems with broken parity, layering, combined Faraday rotation…
We study chains in an $H$-closed topological partially ordered space. We give sufficient conditions for a maximal chain $L$ in an $H$-closed topological partially ordered space such that $L$ contains a maximal (minimal) element. Also we…
Defining P* to be the complete lattice of upsets (ordered by reverse inclusion) of a poset P we give necessary and sufficient conditions on a subset S of P* for P to admit a meet-completion e from P to Q where e preserves the infimum of an…
We give a definition of compactness in L-fuzzy topological spaces and provide a characterization of compact L-fuzzy topological spaces, where L is a complete quasi-monoidal lattice with some additional structures, and we present a version…
This paper covers some recent progress in the study of sg-open sets, sg-compact spaces, N-scattered spaces and some related concepts. A subset $A$ of a topological space $(X,\tau)$ is called sg-closed if the semi-closure of $A$ is included…
In their recent paper on posets with a pseudocomplementation denoted by * the first and the third author introduced the concept of a *-ideal. This concept is in fact an extension of a similar concept introduced in distributive…
This paper is devoted to the study of symplectic manifolds and their connection with Hamiltonian dynamical systems. We review some properties and operations on these manifolds and see how they intervene when studying the complete…
Various characterizations of finite convex geometries are well known. This note provides similar characterizations for possibly infinite convex geometries whose lattice of closed sets is strongly coatomic and lower continuous. Some classes…
We develop Grothendieck's theory of dualizing complexes on finite posets, and its subsequent theory of Cohen-Macaulayness.
This paper studies various completeness properties of the open-point and bi-point-open topologies on the space C(X) of all real-valued continuous functions on a Tychonoff space X. The properties range from complete metrizability to the…
In this paper the concept of a partial cone metric space is investigated, some continuity type theorems, and fixed point theorems of contractive mappings in this generalized setting are proved as well as some theorems related to topological…
Spaces of quasi-invariant measures supplied with different topologies are studied. Their embeddings, projective decompositions, conditions for their metrizability are investigated. Theorems about convergence of nets of quasi-invariant…
Our main goal is to develop a representation for finite distributive nearlattices through certain ordered structures. This representation generalizes the well-known representation given by Birkhoff for finite distributive lattices through…
Building sets were introduced in the study of wonderful compactifications of hyperplane arrangement complements and were later generalized to finite meet-semilattices. Convex geometries, the duals of antimatroids, offer a robust…
We prove a number of dualities between posets and (pseudo)bases of open sets in locally compact Hausdorff spaces. In particular, we show that (1) Relatively compact basic sublattices are finitely axiomatizable. (2) Relatively compact basic…
We provide a unified treatment of several results concerning full groups of ample groupoids and paradoxical decompositions attached to them. This includes a criterion for the full group of an ample groupoid being amenable as well as…