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Tag: complete lattices

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Strong vs weak partitioning – counterexample

By Victor Porton
On February 19, 2010

My problem whether weak partitioning and strong partitioning of a complete lattice are the same was solved by counter-example by François G. Dorais. Remains open whether strong and weak partitioning of a filter object is the same.

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#complete lattices
Filters Open problems

Chain-meet-closed sets on complete lattices

By Victor Porton
On December 12, 2009

Let $latex \mathfrak{A}$ is a complete lattice. I will call a filter base a nonempty subset $latex T$ of $latex \mathfrak{A}$ such that $latex \forall a,b\in T\exists c\in T: (c\le a\wedge c\le b)$. I will call a chain (on $latex \mathfrak{A}$) a…

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#chains#complete lattices
Filters Open problems

Complete lattice generated by a partitioning – finite meets

By Victor Porton
On October 20, 2009

I conjectured certain formula for the complete lattice generated by a strong partitioning of an element of complete lattice. Now I have found a beautiful proof of a weaker statement than this conjecture. (Well, my proof works only in the case of…

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#complete lattices#lattice theory
Filters Open problems

Complete lattice generated by a partitioning of a lattice element

By Victor Porton
On October 20, 2009

In this post I defined strong partitioning of an element of a complete lattice. For me it was seeming obvious that the complete lattice generated by the set $latex S$ where $latex S$ is a strong partitioning is equal to $latex \left\{…

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#complete lattices#lattice theory#polymath proposals
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  • SCIENCE
  • Home
  • Algebraic General Topology
  • Axiomatic Theory of Formulas
  • Limit of a Discontinuous Function
  • More
  • Prize
  • SCIENCE
  • Home
    • Blog
    • Soft
  • Algebraic General Topology
    • Paperback
    • Ebook
    • PDF
  • Axiomatic Theory of Formulas
    • Paperback
    • Ebook
    • PDF
  • Limit of a Discontinuous Function
  • More
    • Donate
    • Review
    • Publish
    • Politics
  • Prize