let X be a banac space & A be a dense G delta set .Show X=A-A?

Answer 1

The set difference A minus A results in the empty set. What did you mean to ask?

Answer 2

from wiki:
In mathematics, Banach spaces (pronounced “Bah-nack”), named after Stefan Banach who studied them, are one of the central objects of study in functional analysis. Many of the infinite-dimensional function spaces studied in functional analysis are examples of Banach spaces.

Definition:
Banach spaces are defined as complete normed vector spaces. This means that a Banach space is a vector space V over the real or complex numbers with a norm ||·|| such that every Cauchy sequence (with respect to the metric d(x, y) = ||x − y||) in V has a limit in V. Since the norm induces a topology on the vector space, a Banach space provides an example of a topological vector space.

Thanks for the oportunity of research this new thing to me. But it is very very abstruse (to me).

Answer 3

According to your question, you started out with nothing and obviously ended up with nothing, back-to-front, front-to-back! What are those things anyway?

Answer 4

please explain first some of the terms...