Boolean Artex Spaces Over Bi-monoids

Abstract

We define Complimented Artex Space over a Bi-monoid. We define Boolean Artex Space over a Bi-monoid. We give an example of a Boolean Artex space over a bi-monoid. We  prove that the homomorphic image of a Complimented Artex Space over a Bi-monoid is a Complimented Artex Space over the Bi-monoid. We also prove that the homomorphic image of a Boolean Artex Space over a bi-monoid M is a Boolean Artex Space over the bi-monoid M.  We also prove that the Cartesian product of Complimented Artex Spaces over a Bi-monoid  is Complimented Artex Space over the Bi-monoid. Finally we prove the Cartesian product of Boolean Artex Spaces over a bi-monoid M is a Boolean Artex Space over the bi-monoid M.

Keywords : Complimented, Distributive Artex Spaces, Homomorphisms