1. The notion of string stability countably infinite interconnection of a class of nonlinear system was introduced.

2. Countably metacompactness are characterized in terms of semi open cover, point wise W refinement, monotonically increasing cover and cushioned refinement.

3. Every weakly countably compact closed convex set in a locally convex space has the quasi-weak drop property.

4. We have proved that difference equation is compatible with partial differential equation and the algorithm is countably stable in our case.

5. In chapter two, we mainly study various properties of relatively almost countably compact subsets.

6. Discusses the computational problem about union of countable infinite of countably infinite sets.

7. A set with cardinality s ＼ s . is said to be denumerable or countably infinite.