Convenient Vector Superspaces Without Norm And Their Properties

Abstract

One of the most widespread methods of modeling nature through elementary particles is to use field theory. In this paper this leads to the study of super spaces and super manifolds based on topological spaces without norm. To generalize and simplify the model to be valid in algebraic setting one needs to express it in category theory.  However this might take time to achieve.  In this paper, we introduce bornology and use it instead of topology in the modeling of elementary particles.  The set with bornology is called by Kriegl and Michor convenient vector space.  When the superstructure is added to it, we get convenient vector superspace.  This space is shown, following Kriegl and Michor to be a Cartesian closed category.  This should show us the way of modeling of field theory using category theory.  This generality however has not been done in this paper.