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Finite atomistic lattices that can be represented as lattices of quasivarieties

K. Adaricheva, Wiesław Dziobiak, V. Gorbunov (1993)

Fundamenta Mathematicae

We prove that a finite atomistic lattice can be represented as a lattice of quasivarieties if and only if it is isomorphic to the lattice of all subsemilattices of a finite semilattice. This settles a conjecture that appeared in the context of [11].

Finite orders and their minimal strict completion lattices

Gabriela Hauser Bordalo, Bernard Monjardet (2003)

Discussiones Mathematicae - General Algebra and Applications

Whereas the Dedekind-MacNeille completion D(P) of a poset P is the minimal lattice L such that every element of L is a join of elements of P, the minimal strict completion D(P)∗ is the minimal lattice L such that the poset of join-irreducible elements of L is isomorphic to P. (These two completions are the same if every element of P is join-irreducible). In this paper we study lattices which are minimal strict completions of finite orders. Such lattices are in one-to-one correspondence with finite...

Finite topological spaces.

Juan A. Navarro González (1990)

Extracta Mathematicae

We show that the study of topological T0-spaces with a finite number of points agrees essentially with the study of polyhedra, by means of the geometric realization of finite spaces. In this paper all topological spaces are assumed to be T0.

Fixed point results on a metric space endowed with a finite number of graphs and applications

Hajer Argoubi, Bessem Samet, Mihai Turinici (2014)

Czechoslovak Mathematical Journal

In this paper, we consider self-mappings defined on a metric space endowed with a finite number of graphs. Under certain conditions imposed on the graphs, we establish a new fixed point theorem for such mappings. The obtained result extends, generalizes and improves many existing contributions in the literature including standard fixed point theorems, fixed point theorems on a metric space endowed with a partial order and fixed point theorems for cyclic mappings.

Fixed points of fuzzy monotone maps

Ismat Beg (1999)

Archivum Mathematicum

The existence of fixed points for monotone maps on the fuzzy ordered sets under suitable conditions is proved.

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