Zerotoepsilon

As we know that all cyclic groups are generated by a single element but what about non-cyclic groups?    How far any non-cyclic group is in the number of generators to cyclic groups? After going through the article (link attached below) you will know some interesting facts as well as the answer to the above questions.  Generating Set for Various Groups Click on the above link.

Open set(so closed set) are building blocks for a Topological space.  A random subset of a topological space (X,  τ)  need not be either open or closed but there is always an open and closed set associated with it. Let A   X where (X,  τ ) is a topological space. We know that  Φ  is an open set i.e. contained in every subset of X. Can we go for an open set larger than  Φ , contained in A? Similiarly, the smallest open set in which contain A. Same thing we can do for the closed set, largest and smallest set respectively contained and containing A. These questions give rise to the concept of Closure and Interior. Closure of A   X  -:  The closure of A in (X,  τ ), is defined as the smallest closed set, which contains A. For example, closure of [0,2)  is [0,2] and closure of set S = {1/n : n    } is S   {0} with usual topology on  .  Some of the text use the following definition of closure as A   A', which is not an intuitive way of defining a new concept. Of course, it is e