Boundedness Theorem for Continuous Functions in the Perplex Number-plane

Continuous function theory is a very important part of functional theory. In this paper, this article research the properties of continuous functions in the P-plane, which are commutative rings containing zero factors generated by two real number. This article overcome the difficulties arising from the zero factorisation of P-numbers and prove that continuous functions in the P-plane are bounded by the decomposition of P-numbers and a geometric interpretation is given for the boundedness of continuous functions in the P-plane. For continuous Perplex functions that satisfy zero factor decomposition, based on the decomposition of Perplex numbers, we obtain the continuous boundedness theorem for Perplex functions. This will further provide a theoretical foundation and research impetus for P-analysis and give impetus to applications of the theory of continuous functions in the p-plane in physics.