We develop a theory of stratified $LM$-filters which generalizes the theory of stratified $L$-filters. Our stratification condition explicitly depends on a suitable mapping between the lattices $L$ and $M$. If $L$ and $M$ are identical and the mapping is the identity mapping, then we obtain the theory of stratified $L$-filters. Based on the stratified $LM$-filters, a general theory of lattice-v...

we show that the character space of the vector-valued lipschitz algebra $lip^{alpha}(x, e)$ of order $alpha$ is homeomorphic to the cartesian product $xtimes m_e$ in the product topology, where $x$ is a compact metric space and $e$ is a unital commutative banach algebra. we also characterize the form of each character on $lip^{alpha}(x, e)$. by appealing to the injective tensor product, we then...

The ‘the’ in the title hides a subtlety. A metric space induces not one but four topologies - by means of open sets, closed closure, and interior they just so happen to coincide. agreement between these structures arising from function d:X×X→[0,∞] is due combination axioms lattice structure [0,∞]. Further motivation materializes Lawvere's observation 1973 effect that (slightly generalized) cate...

Abstract. Let L be a lattice and M a bounded distributive lattice. Let ConL denote the congruence lattice of L, P (M) the Priestley dual space of M , and L (M) the lattice of continuous order-preserving maps from P (M) to L with the discrete topology. It is shown that Con(L ) ∼= (ConL) P (ConM) Λ , the lattice of continuous order-preserving maps from P (ConM) to ConL with the Lawson topology. V...

an object $x$ of a category $mathbf{c}$ with finite limits is called exponentiable if the functor $-times x:mathbf{c}rightarrow mathbf{c}$ has a right adjoint. there are many characterizations of the exponentiable  spaces in the category $mathbf{top}$ of topological spaces. here, we study the exponentiable objects in the category $mathbf{stop}$ of soft topological spaces which is a generalizati...

In this paper a particular case of z-ideals, called strongly z-ideal, is defined by introducing zero sets in pointfree topology. We study strongly z-ideals, their relation with z-ideals and the role of spatiality in this relation. For strongly z-ideals, we analyze prime ideals using the concept of zero sets. Moreover, it is proven that the intersection of all zero sets of a prime ideal of C(L),...

This work introduces a new data structure, called Lattice-Valued Binary Decision Diagrams (or LVBDD for short), for the compact representation and manipulation of functions of the form θ : 2 7→ L, where P is a finite set of Boolean propositions and L is a finite distributive lattice. Such functions arise naturally in several verification problems. LVBDD are a natural generalisation of multi-ter...

We found that the differential topology of the lattice-system Ising model determines whether there can be the continuous phase transition, The geometric topology of the space the lattice-system is embedded in determines whether the system can become ordered. If the system becomes ordered it may not admit the continuous phase transition. The spin-projection orientations are strongly influenced b...

In multi-valued model checking, a temporal logic formula is interpreted relative to a structure not as a truth value but as a lattice element. In this paper we present new algorithms for multi-valued model checking. We first show how to reduce multi-valued model checking with any distributive DeMorgan lattice to standard, two-valued model checking. We then present a direct, automata-theoretic a...

This paper is an investigation of $L$-dual frames with respect to a function-valued inner product, the so called $L$-bracket product on $L^{2}(G)$, where G is a locally compact abelian group with a uniform lattice $L$. We show that several well known theorems for dual frames and dual Riesz bases in a Hilbert space remain valid for $L$-dual frames and $L$-dual Riesz bases in $L^{2}(G)$.