$Q$-Meromorphic Functions, Quantums sets and Homomorphisms of the Quantum Plane

Abstract

In this paper which is the completion of [1], we construct the $A_0(q)$-algebra of $Q$-meromorphic functions on the quantum plane. This is the largest non-commutative, associative, $A_0(q)$-algebra of functions constructed on the quantum plane. We also define the notion of quantum subsets of R$^2$ which is a generalization of the notion of quantum disc and charactrize some of their properties. In the end we study the $Q$-homomorphisms of the quantum plane.