The number of complements of a topology on \(n\) points is at least \(2^ n\) (except for some special cases)

DOI10.1016/0012-365X(95)00004-GzbMath0852.05008OpenAlexW2169001064WikidataQ126590607 ScholiaQ126590607MaRDI QIDQ1918536

Jason I. Brown, W. Stephen Watson

Publication date: 25 November 1996

Published in: Discrete Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0012-365x(95)00004-g

zbMATH Keywords

complementstopological spacepreordered sets

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) Combinatorics of partially ordered sets (06A07) Several topologies on one set (change of topology, comparison of topologies, lattices of topologies) (54A10)

Related Items

Complementation in the lattice of locally convex topologies, The lattice of functional Alexandroff topologies, Complements of convex topologies on products of finite totally ordered spaces, Open problems in topology., Properties of distance spaces with power triangle inequalities, Computer programing for construction and enumeration of all regular topologies and equivalence relations on finite sets, Unnamed Item

Cites Work

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• Self complementary topologies and preorders
• Counting finite posets and topologies
• The number of complements in the lattice of topologies on a fixed set
• Partial order complementation graphs
• Mutually complementary partial orders
• On the number of open sets of finite topologies
• Finite topologies and Hamiltonian paths
• An extremal problem for finite topologies and distributive lattices
• Struktur- und Anzahlformeln für Topologien auf endlichen Mengen
• A Machine Representation of Finite T ₀ Topologies
• On the Lattice of Topologies
• The Lattice of Topologies: Structure and Complementation
• The Lattice of all Topologies is Complemented
• On the computer enumeration of finite topologies
• Multiple complementation in the lattice of topologies
• Infinite complementation in the lattice of topologies
• The Number of Finite Topologies
• Families of Mutually Complementary Topologies