Categories of closure spaces and corresponding lattices

Claude-Alain Faure

Displaying similar documents to “Categories of closure spaces and corresponding lattices”

On the theory of Baer lattices

M. Stem (1982)

Banach Center Publications

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A topological representation of polarity lattices.

Hartung, G., Kamara, M., Săcărea, C. (1999)

Acta Mathematica Universitatis Comenianae. New Series

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Representation of complete lattices by sets

Büchi, J. Richard (1952)

Portugaliae mathematica

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How many four-generated simple lattices

Ivan Rival, Bill Sands (1982)

Banach Center Publications

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The amalgamation property of varieties determined by primitive lattices

Václav Slavík (1980)

Commentationes Mathematicae Universitatis Carolinae

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Stone Lattices

Adam Grabowski (2015)

Formalized Mathematics

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The article continues the formalization of the lattice theory (as structures with two binary operations, not in terms of ordering relations). In the paper, the notion of a pseudocomplement in a lattice is formally introduced in Mizar, and based on this we define the notion of the skeleton and the set of dense elements in a pseudocomplemented lattice, giving the meet-decomposition of arbitrary element of a lattice as the infimum of two elements: one belonging to the skeleton, and the...

Lattices of Scott-closed sets

Weng Kin Ho, Dong Sheng Zhao (2009)

Commentationes Mathematicae Universitatis Carolinae

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A dcpo $P$ is continuous if and only if the lattice $C (P)$ of all Scott-closed subsets of $P$ is completely distributive. However, in the case where $P$ is a non-continuous dcpo, little is known about the order structure of $C (P)$ . In this paper, we study the order-theoretic properties of $C (P)$ for general dcpo’s $P$ . The main results are: (i) every $C (P)$ is C-continuous; (ii) a complete lattice $L$ is isomorphic to $C (P)$ for a complete semilattice $P$ if and only if $L$ is weak-stably C-algebraic; (iii) for any two complete...