Curiosities concerning Weak Topology in Hubert Space.

The article focuses on the issues concerning the weak topology in Hilbert space. It thoroughly discusses the features of the weak topology in H. An example is presented to further elaborate on the topology stating that in the strong topology in H is separable and satisfies the second axiom of countability. It further explains that the set of finite sum expansions with complex rational coefficients is countable and dense in H and that open balls with radius centered at particular points compose a countable base for the strong topology. Several theorems, corollaries and alternate proof is presented.