No CrossRef data available.
Article contents
On the Lattice of Primitive Convergence Structures
Published online by Cambridge University Press: 20 November 2018
Extract
Let S be any set and denote by F(S) the collection of all fiters on S. The collection A(S) of all mappings from F(S) to 2s, 2s being ordered by the dual of its usual ordering, may be regarded as a product of complete Boolean algebras and is, therefore, a complete atomic Boolean algebra [4]. A(S) is called the lattice of primitive convergence structures on S. If q ∈ A(S) and , then is said to q-converge to a point x ∈ S if . The collection of all topologies on S may be identified with a subset of A(S); this subset of A(S) will be denoted by T(S). A more specialized class of primitive convergence structures, and one which properly contains T(S), is C(S), the subcomplete lattice of all convergence structures on S.
- Type
- Research Article
- Information
- Copyright
- Copyright © Canadian Mathematical Society 1971