• Bounded Artex Spaces Over Bi-monoids and Artex Space Homomorphisms

Abstract

We introduce Some Special Artex Spaces over bi-monoids namely Complete Artex Spaces over bi-monoids , Lower Bounded Artex Spaces over bi-monoids, Upper Bounded Artex Spaces over bi-monoids, Bounded Artex Spaces over bi-monoids ,Artex Space homomorphism, Artex Space epimorphism, Artex Space monomorphism, and Artex Space isomorphism. We prove the homomorphic image of a Lower Bounded Artex Space over a bi-monoid is a Lower Bounded Artex Space over the bi-monoid and the homomorphic image of an Upper Bounded Artex Space over a bi-monoid is an Upper Bounded Artex Space over the bi-monoid and in general the homomorphic image of a Bounded Artex Space over a bi-monoid is a Bounded Artex Space over the bi-monoid. We prove under the Artex Space homomorphism the least element goes to the least element and the greatest element goes to the greatest element. Also we prove the cartesian product of Lower Bounded Artex Spaces over a bi-monoid is a Lower Bounded Artex Space over the bi-monoid and the Cartesian product of Upper Bounded Artex Spaces over a bi-monoid is an Upper Bounded Artex Space over the bi-monoid and in general the Cartesian product of Bounded Artex Spaces over a bi-monoid is a Bounded Artex Space over the bi-monoid.