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A Primer on Galois Connections
TLDR
The rudiments of the theory of Galois connections (or residuation theory, as it is sometimes called) are provided, together with many examples and applications, that can be used as an effective research tool throughout mathematics and related areas. Expand
Z-Continuous Posets and Their Topological Manifestation
  • M. Erné
  • Computer Science, Mathematics
  • Appl. Categorical Struct.
  • 1 June 1999
TLDR
It turns out that for arbitrary subset selections Z, a poset P is strongly Z-continuous iff its Z-join ideal completion Z∨ P is Z-ary and completely distributive. Expand
Counting finite posets and topologies
A refinement of an algorithm developed by Culberson and Rawlins yields the numbers of all partially ordered sets (posets) with n points and k antichains for n≤11 and all relevant integers k. UsingExpand
The category of Z-continuous posets
Complete distriburivity is an old theme in lattice theory: the basic results were already proved in the early fifties by G.N. Raney. Some new features of completely distributive lattices have bet..Expand
On the cardinalities of finite topologies and the number of antichains in partially ordered sets
  • M. Erné
  • Mathematics, Computer Science
  • Discret. Math.
  • 1981
TLDR
The average cardinality of (T"0) topologies on n points is shown to be 2^n^2^+^O^(^l^o^g^ ^n^). Expand
Categories of Locally Hypercompact Spaces and Quasicontinuous Posets
  • M. Erné
  • Computer Science, Mathematics
  • Appl. Categorical Struct.
  • 9 August 2018
TLDR
This work describes their patch spaces as hyperconvex and hyperregular pospaces in which every monotone net has a supremum to which it converges and provides topological generalizations of known facts for quasicontinuous posets. Expand
Bigeneration in complete lattices and principal separation in ordered sets
By a recent observation of Monjardet and Wille, a finite distributive lattice is generated by its doubly irreducible elements iff the poset of all join-irreducible elements has a distributiveExpand
Algebraic Ordered Sets and Their Generalizations
We study order-theoretical, algebraic and topological aspects of compact generation in ordered sets. Today, algebraic ordered sets (a natural generalization of algebraic lattices) have their placeExpand
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