Coatoms of the lattice of funcoids (Solved)

 Importance: Low ✭
 Author(s): Porton, Victor
 Subject: Topology
 Keywords: atoms coatoms funcoids
 Posted by: porton on: April 24th, 2014
 Solved by: Porton, Victor
Problem   Let and be infinite sets. Characterize the set of all coatoms of the lattice of funcoids from to . Particularly, is this set empty? Is a coatomic lattice? coatomistic lattice?

See Algebraic General Topology for definitions of used concepts.

Solved:

Coatoms of are principal funcoids corresponding to binary relations of the form where , .

The set of funcoids is atomic but not atomistic.

See new version of the book Algebraic General Topology.

Bibliography

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