Related papers: Some results on $L$-complete lattices
The state spaces of machines admit the structure of time. A homotopy theory respecting this additional structure can detect machine behavior unseen by classical homotopy theory. In an attempt to bootstrap classical tools into the world of…
In this paper we primarily study monomial ideals and their minimal free resolutions by studying their associated LCM lattices. In particular, we formally define the notion of coordinatizing a finite atomic lattice P to produce a monomial…
We introduce a pointfree theory of convergence on lattices and coframes. A convergence lattice is a lattice $L$ with a monotonic map $\lim_L$ from the lattice of filters on $L$ to $L$, meant to be an abstract version of the map sending…
We study FTOP(L), a fuzzy category with fuzzy functions in the role of morphisms. This category has the same objects as the category L-TOP of Chang-Goguen L-topological spaces,but an essentially wider class of morphisms - so called fuzzy…
For a given partially ordered set (poset) and a given family of mappings of the poset into itself, we study the problem of the description of joint fixed points of this family. Well-known Tarski's theorem gives the structure of the set of…
Let $\phi: G \rightarrow H$ be a group homomorphism such that $H$ is a totally disconnected locally compact (t.d.l.c.) group and the image of $\phi$ is dense. We show that all such homomorphisms arise as completions of $G$ with respect to…
We define several sorts of mappings on a poset like monotone, strictly monotone, upper cone preserving and variants of these. Our aim is to characterize posets in which some of these mappings coincide. We define special mappings determined…
We generalize the notion of complete binary relation on complete lattice to residuated lattice valued ordered sets and show its properties. Then we focus on complete fuzzy tolerances on fuzzy complete lattices and prove they are in…
The Fine interior $F(P)$ of a $d$-dimensional lattice polytope $P \subset {\Bbb R}^d$ is the set of all points $y \in P$ having integral distance at least $1$ to any integral supporting hyperplane of $P$. We call a lattice polytope…
Let I be a dense linear order with a left endpoint but no right endpoint. We consider the lattice L(I) of finite unions of closed intervals of I. This lattice arises naturally in the setting of o-minimality, as these are precisely the…
Closure operators are very useful tools in several areas of classical mathematics and in general category theory. In fuzzy set theory, fuzzy closure operators have been studied by G. Gerla (1966). These works generally define a fuzzy subset…
Two years ago, I characterized the order $\Princl L$ of principal congruences of a bounded lattice $L$ as a bounded order. If $K$ and $L$ are bounded lattices and $\gf$ is a \zo homomorphism of $K$ into~$L$, then there is a natural isotone…
This article explores several fundamental aspects of fuzzy $\mathscr{F}$-metric spaces and their applications in mathematical analysis. We investigate some essential properties concerning compactness and total boundedness in fuzzy…
This paper first gives a necessary and sufficient condition that a lattice $L$ can be represented as the collection of all up-sets of a poset. Applying the condition, it obtains a necessary and sufficient condition that a lattice can be…
Crisp and $L$-fuzzy ambiguous representations of closed subsets of one space by closed subsets of another space are introduced. It is shown that, for each pair of compact Hausdorff spaces, the set of (crisp or $L$-fuzzy) ambiguous…
Partially ordered sets labeled with k labels (k-posets) and their homomorphisms are examined. We give a representation of directed graphs by k-posets; this provides a new proof of the universality of the homomorphism order of k-posets. This…
We prove two results concerning an Ulam-type stability problem for homomorphisms between lattices. One of them involves estimates by quite general error functions; the other deals with approximate (join) homomorphisms in terms of certain…
For a partially ordered set P, we denote by Co(P) the lattice of order-convex subsets of P. We find three new lattice identities, (S), (U), and (B), such that the following result holds. Theorem. Let L be a lattice. Then L embeds into some…
Since the theory of rough sets was introduced by Zdzislaw Pawlak, several approaches have been proposed to combine rough set theory with fuzzy set theory. In this paper, we examine one of these approaches, namely fuzzy rough sets with crisp…
Covering is a common type of data structure and covering-based rough set theory is an efficient tool to process this data. Lattice is an important algebraic structure and used extensively in investigating some types of generalized rough…