Home » Subject » Topology
Importance: Low ✭
Author(s): Porton, Victor
Subject: Topology
Keywords: atoms
coatoms
funcoids
Recomm. for undergrads: no
Posted by: porton
on: April 24th, 2014
Solved by: Porton, Victor
Problem   Let $ A $ and $ B $ be infinite sets. Characterize the set of all coatoms of the lattice $ \mathsf{FCD}(A;B) $ of funcoids from $ A $ to $ B $. Particularly, is this set empty? Is $ \mathsf{FCD}(A;B) $ a coatomic lattice? coatomistic lattice?

See Algebraic General Topology for definitions of used concepts.

Solved:

Coatoms of $ \mathsf{FCD}(A;B) $ are principal funcoids corresponding to binary relations of the form $ (A\times B)\setminus(\{x\}\times\{y\}) $ where $ x\in A $, $ y\in B $.

The set of funcoids is atomic but not atomistic.

See new version of the book Algebraic General Topology.

Bibliography

*Blog post with this question


* indicates original appearance(s) of problem.
add new comment

Reply

Comments are limited to a maximum of 1000 characters.
More information about formatting options