| Article ID | Journal | Published Year | Pages | File Type |
|---|---|---|---|---|
| 4660042 | Topology and its Applications | 2008 | 6 Pages |
Abstract
For a given set X, the set F(X) of all maps from X to X forms a semigroup under composition. A subsemigroup S of F(X) is said to be saturated if for each x∈X there exists a set Ox⊆X with x∈Ox such that . It is shown that there exists a one-to-one correspondence between principal topologies on X and saturated subsemigroups of F(X). Some properties of principal topologies on X and the corresponding properties of their associated saturated subsemigroups of F(X) are discussed.
Related Topics
Physical Sciences and Engineering
Mathematics
Geometry and Topology
