Struktur- und Anzahlformeln für Topologien auf endlichen Mengen

DOI10.1007/BF01173716zbMath0269.54001MaRDI QIDQ2563321

Marcel Erné

Publication date: 1974

Published in: Manuscripta Mathematica (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/154212

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) Several topologies on one set (change of topology, comparison of topologies, lattices of topologies) (54A10) Lower separation axioms ((T_0)--(T_3), etc.) (54D10) Higher separation axioms (completely regular, normal, perfectly or collectionwise normal, etc.) (54D15)

Related Items (23)

Partial order complementation graphs ⋮ Structural and numerical studies of some topological properties for Alexandroff spaces ⋮ The number of complements of a topology on \(n\) points is at least \(2^ n\) (except for some special cases) ⋮ On some topological properties in the class of Alexandroff spaces ⋮ On some formulas in the problem of enumeration of finite labeled topologies ⋮ On the cardinalities of finite topologies and the number of antichains in partially ordered sets ⋮ Self complementary topologies and preorders ⋮ Counting finite posets and topologies ⋮ On support sets of acyclic and transitive digraphs ⋮ On recurrence relation in the problem of enumeration of finite posets ⋮ Solving computational tasks on finite topologies by means of relation algebra and the \textsc{RelView} tool ⋮ On the cardinality of the \(T_0\)-topologies on a finite set ⋮ The number of convex sets in a product of totally ordered sets ⋮ Obtainable sizes of topologies on finite sets ⋮ Pictures from Mongolia. Extracting the top elements from a partially ordered set ⋮ Algebras defined from ordered sets and the varieties they generate ⋮ On The Number Of Topologies On A Finite Set ⋮ On recursion relations in the problem of enumeration of posets ⋮ A framework for the systematic determination of the posets on \(n\) points with at least \(\tau \cdot 2^n\) downsets ⋮ A generalization of a theorem of Erné about the number of posets with a fixed antichain ⋮ A relation in finite topologies ⋮ Periodicity of residues of the number of finite labeled topologies ⋮ On the spectrum and number of convex sets in graphs

Cites Work

• Finite Topological Spaces
• Quasi-Orderings and Topologies on Finite Sets
• On the number of topologies definable for a finite set
• On the computer enumeration of finite topologies
• Note on Finite Topological Spaces
• The Number of Finite Topologies
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