PACKAGE CONTRACTIONS AND ITS RELATIONSHIP TO THE GENERAL CONTRACTION
Dong Zhang · Chinese Journal of Computers · 1999
This paper firstly proves that one of the supplementary postulates for package contractions is inconsistent with the its basic postulates through a counterexample, which means that the postulate system for package contractions is not consistent. By modifying the postulates for package contractions, some evident defect in the original system is remedied. It is proved that if a package contraction function satisfies the modified postulates, it will be a maxichoice package contraction function. Even though the evident defect is eliminated, a more profound paradox still exists in the modified system. Finally, the paper gives a relationship between the package contraction and the general contraction in order to show that the former can be partially defined and substituted by the latter.