The number of complements in the lattice of topologies on a fixed set

DOI10.1016/0166-8641(94)90112-0zbMath0797.54001OpenAlexW1979912753MaRDI QIDQ1313925

W. Stephen Watson

Publication date: 19 October 1994

Published in: Topology and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0166-8641(94)90112-0

zbMATH Keywords

complementationlattice of topologies

Mathematics Subject Classification ID

Several topologies on one set (change of topology, comparison of topologies, lattices of topologies) (54A10) Cardinality properties (cardinal functions and inequalities, discrete subsets) (54A25) Complemented lattices, orthocomplemented lattices and posets (06C15) Counterexamples in general topology (54G20) Consistency and independence results in general topology (54A35)

Related Items (14)

Mutually complementary partial orders ⋮ Partial order complementation graphs ⋮ Complementation in the lattice of locally convex topologies ⋮ The number of complements of a topology on \(n\) points is at least \(2^ n\) (except for some special cases) ⋮ Transversal, \(T_{1}\)-independent, and \(T_{1}\)-complementary topologies ⋮ The lattice of functional Alexandroff topologies ⋮ Infima and complements in the lattice of quasi-uniformities ⋮ Maximal complements in the lattices of pre-orders and topologies. ⋮ Uniqueness conditions of the representation of a topology in \(Top(X)\) ⋮ Finite intervals in the lattice of topologies ⋮ Self complementary topologies and preorders ⋮ Unnamed Item ⋮ Atoms, anti-atoms and complements in the lattice of quasi-uniformities ⋮ Self-transversal spaces and their discrete subspaces

Cites Work

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