In infinite topological Fort space X, for nonempty subsets C, D of X in the following text we answer to this question "Is there any λ and Top-design C − (X, D, λ) of type i?" for i = 1, 2, 3, 4. We prove there exist λ and C − (X, D, λ), Top-design of type 2 (resp. type 4) if and only if C can be embedded into D.

In the following text we introduce the notion of chaoticity modulo an ideal in the sense of Li-Yorke in topological transformation semigroups and bring some of its elementary properties. We continue our studies by characterizing a class of abelian infinite Li-Yorke chaotic Fort transformation groups and show all of the elements of the above class is co-decomposable to non-Li-Yorke chaotic transformation groups.

No abstract