Marcel Erné

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A subset selection Z assigns to each partially ordered set P a certain collection ZP of subsets. The theory of topological and of algebraic (i.e. finitary) closure spaces extends to the general Z-level, by replacing finite or directed sets, respectively, with arbitrary ‘Z-sets’. This leads to a theory of Z-union completeness, Z-arity, Z-soberness etc.(More)
We investigate the numbers dk of all (isomorphism classes of) distributive lattices with k elements, or, equivalently, of (unlabeled) posets with k antichains. Closely related and useful for combinatorial identities and inequalities are the numbers vk of vertically indecomposable distributive lattices of size k. We present the explicit values of the numbers(More)
We provide the appropriate common ‘(pre)framework’ for various central results of domain theory and topology, like the Lawson duality of continuous domains, the Hofmann–Lawson duality between continuous frames and locally compact sober spaces, the Hofmann–Mislove theorems about continuous semilattices of compact saturated sets, or the theory of stably(More)
Many graph-theoretical problems involve the study of cliques, i .e ., complete subgraphs (not necessarily maximal) . In this context the following combinatorial problem arises naturally: For which numbers n and c is there a graph with n vertices and exactly c cliques? For fixed n, let G(n) denote the set of all such `clique numbers' c . Since each singleton(More)
Klaus Ambos-Spies, Heidelberg Klaus Meer, Cottbus Marat M. Arslanov, Kazan Wolfram Pohlers, Münster Günter Asser, Greifswald Pavel Pudlak, Prague John T. Baldwin, Chicago Andrzej Rosłanowski, Omaha Douglas S. Bridges, Canterbury Jörg Rothe, Düsseldorf Ramon Jansana, Barcelona Wilfried Sieg, Pittsburgh Carl G. Jockusch, Urbana Stephen G. Simpson, State(More)
From the work of Simmons about nuclei in frames it follows that a topological space X is scattered if and only if each congruence Θ on the frame of open sets is induced by a unique subspace A so that Θ = {(U, V ) |U ∩A = V ∩A}, and that the same holds without the uniqueness requirement iff X is weakly scattered (corrupt). We prove a seemingly similar but(More)