The Lattice of Topologies: Structure and Complementation

DOI10.2307/1994555zbMath0139.15905OpenAlexW4253176183WikidataQ56336627 ScholiaQ56336627MaRDI QIDQ5514262

A. K. Steiner

Publication date: 1966

Full work available at URL: https://doi.org/10.2307/1994555

zbMATH Keywords

topology

Related Items (55)

Mutually complementary partial orders ⋮ Partial order complementation graphs ⋮ Complementation in the lattice of locally convex topologies ⋮ On the product of primal spaces ⋮ Intervals in lattices of quasiorders ⋮ 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 ⋮ Complementation in the lattice of equivalence relations ⋮ Alexandroff topologies and monoid actions ⋮ A unifying study between modal-like operators, topologies and fuzzy sets ⋮ Complements of convex topologies on products of finite totally ordered spaces ⋮ The Hopf algebra of finite topologies and mould composition ⋮ General topology (set-theoretic trend) ⋮ Smallness in topology ⋮ Tychonoff expansions in which a given set is open ⋮ Topological properties of prime filters in MTL-algebras and fuzzy set representations for MTL-algebras ⋮ Upper neighbours of Čech closure operators ⋮ Maximal complements in the lattices of pre-orders and topologies. ⋮ A method of representing rough sets system determined by quasi orders ⋮ Topologies on products of partially ordered sets. I: Interval topologies ⋮ Topological quandles up to four elements ⋮ The categories of flows of Set and Top ⋮ Generalizations of some ordinary and extreme connectedness properties of topological spaces to relator spaces ⋮ Transversal group topologies on non-Abelian groups ⋮ Necessary and possible preference structures ⋮ Commutative unary algebras with join-semidistributive topology lattices ⋮ Uniqueness conditions of the representation of a topology in \(Top(X)\) ⋮ Spectral primal spaces ⋮ A PROSET STRUCTURE INDUCED FROM HOMOTOPY CLASSES OF MAPS AND A CLASSIFICATION OF FIBRATIONS ⋮ Transversal and \(T_1\)-independent topologies and the Alexandroff duplicate ⋮ On resolvable primal spaces ⋮ Families of Mutually Complementary Topologies ⋮ On quasiorder lattices and topology lattices of algebras ⋮ Self complementary topologies and preorders ⋮ Algebraic Representation, Dualities and Beyond ⋮ On the lattice of fuzzy topologies. I ⋮ On the hierarchy of d-structures ⋮ Unnamed Item ⋮ Computer programing for construction and enumeration of all regular topologies and equivalence relations on finite sets ⋮ Submaximal and door compactifications ⋮ A Stone-type duality for \(s T_0\) stratified Alexandrov \(L\)-topological spaces ⋮ On the lattices of \(L\)-topologies ⋮ Unnamed Item ⋮ Doubling bialgebras of finite topologies ⋮ On the Lattice of Stratified Principal L-topologies ⋮ Locally Modular Lattices and Locally Distributive Lattices ⋮ Commutative unary algebras with modular and distributive topology lattices ⋮ Maps generating the same primal space ⋮ \(k\)-primal spaces ⋮ Unnamed Item ⋮ Epistemic foundations for set-algebraic representations of knowledge ⋮ The number of complements in the lattice of topologies on a fixed set ⋮ Some results on modal axiomatization and definability for topological spaces ⋮ Independent group topologies on abelian groups

Cites Work

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• Das Halbordnungssystem der topologischen Räume auf einer Menge
• On the Lattice of Topologies
• Remarks on Complementation in the Lattice of all Topologies
• The complement of a topology of some topological groups
• Ultrafilters and Compactification of Uniform Spaces
• Beiträge zur Filtertheorie. I
• On the Characterization of the Lattice of Topologies^*
• Über den Ultrafilterraum

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