Notes on Exact Meets and Joins

نویسندگان

  • Richard N. Ball
  • Jorge Picado
  • Ales Pultr
چکیده

An exact meet in a lattice is a special type of infimum characterized by, inter alia, distributing over finite joins. In frames, the requirement that a meet is preserved by all frame homomorphisms makes for a slightly stronger property. In this paper these concepts are studied systematically, starting with general lattices and proceeding through general frames to spatial ones, and finally to an important phenomenon in Scott topologies.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Topological Duality and Lattice Expansions Part II: Lattice Expansions with Quasioperators

Lattices have many applications in mathematics and logic, in which they occur together with additional operations. For example, in applications of Hilbert spaces, one is often concerned with the lattice of closed subspaces of a fixed space. This lattice is not distributive, but there is an operation taking a given subspace to its orthogonal subspace. More generally, ortholattices are lattices w...

متن کامل

A note on infinitely distributive inverse semigroups

By an infinitely distributive inverse semigroup will be meant an inverse semigroup S such that for every subset X ⊆ S and every s ∈ S, if ∨ X exists then so does ∨ (sX), and furthermore ∨ (sX) = s ∨ X. One important aspect is that the infinite distributivity of E(S) implies that of S; that is, if the multiplication of E(S) distributes over all the joins that exist in E(S) then S is infinitely d...

متن کامل

An Algebraic Approach to Stable Domains

Day [75] showed that the category of continuous lattices and maps which preserve directed joins and arbitrary meets is the category of algebras for a monad over Set, Sp or Pos, the free functor being the set of filters of open sets. Separately, Berry [78] constructed a cartesian closed category whose morphisms preserve directed joins and connected meets, whilst Diers [79] considered similar fun...

متن کامل

Lattice Completion Algorithms for Distributed Computations

A distributed computation is usually modeled as a finite partially ordered set (poset) of events. Many operations on this poset require computing meets and joins of subsets of events. The lattice of normal cuts of a poset is the smallest lattice that embeds the poset such that all meets and joins are defined. In this paper, we propose new algorithms to construct or enumerate the lattice of norm...

متن کامل

Completions of Ordered Algebraic Structures: A Survey

Introduction The ordered field of rationals (Q, ≤, +, ·) is an ordered algebraic structure — i.e. a poset with additional operations. to complete the rationals — that is, to embed the rationals into a structure where every (bounded) subset has a join and meet. This is a very good completion as it preserves all existing joins and meets as well as many algebraic properties. Introduction Ordered a...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:
  • Applied Categorical Structures

دوره 22  شماره 

صفحات  -

تاریخ انتشار 2014