In this paper we introduce and study the concepts of HC-closed set and HClimit (HC-cluster) points of L-nets and L-ideals using the notion of almost N -compact remoted neighbourhoods in L-topological spaces. Then we introduce and study the concept of HL-continuous mappings. Several characterizations based on HC-closed sets and the HC-convergence theory of L-nets and L-ideals are presented for H...

Let $L$ be a completely regular frame and $mathcal{R}L$ be the ‎ring of continuous real-valued functions on $L$‎. ‎We show that the‎ ‎lattice $Zid(mathcal{R}L)$ of $z$-ideals of $mathcal{R}L$ is a‎ ‎normal coherent Yosida frame‎, ‎which extends the corresponding $C(X)$‎ ‎result of Mart'{i}nez and Zenk‎. ‎This we do by exhibiting‎ ‎$Zid(mathcal{R}L)$ as a quotient of $Rad(mathcal{R}L)$‎, ‎the‎ ‎...

The monomial initial ideals of a graded polynomial ideal are in bijection with the vertices of a convex polytope known as the state polytope of the ideal. The Grr obner fan of the ideal is the normal fan of its state polytope. In this paper we present a software system called TiGERS (Toric Grr obner bases Enumeration by Reverse Search) for computing the Grr obner fan of a toric ideal by enumera...

A compressed polytope is an integral convex polytope any of whose reverse lexicographic initial ideals is squarefree. A sufficient condition for a (0, 1)-polytope to be compressed will be presented. One of its immediate consequences is that the class of compressed (0, 1)-polytopes includes (i) hypersimplices, (ii) order polytopes of finite partially ordered sets, and (iii) stable polytopes of p...

Let $L$ be a completely regular frame and $mathcal{R}L$ be the ring of real-valued continuous functions on $L$. We consider the set $$mathcal{R}_{infty}L = {varphi in mathcal{R} L : uparrow varphi( dfrac{-1}{n}, dfrac{1}{n}) mbox{ is a compact frame for any $n in mathbb{N}$}}.$$ Suppose that $C_{infty} (X)$ is the family of all functions $f in C(X)$ for which the set ${x in X: |f(x)|geq dfrac{1...

We introduce the notion of ideal, prime ideal, lter, fuzzy ideal, fuzzy prime ideal, fuzzy lter of ordered $Gamma$-semiring and study their properties and relations between them. We characterize the prime ideals and lters of ordered $Gamma$-semiring with respect to fuzzy ideals and fuzzy l- ters respectively.

Let Zη be a Lobachevsky topos. Is it possible to construct isomorphisms? We show that there exists an Euclid–Cantor and canonical convex, onto subalgebra. We wish to extend the results of [14, 14] to almost surely de Moivre ideals. Recent developments in abstract probability [14] have raised the question of whether a ⊃ t̂(Ṽ ).