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The article presents several examples of different mathematical structures and interprets their properties related to the existence of universal functions. In this context, relations between the problem of totality of elements and possible forms of universal functions are analyzed. Furthermore, some global and local aspects of the mentioned functional systems are distinguished and compared. In addition, the paper attempts to link universality and totality with the dynamic and static properties of mathematical objects and to consider the problem of limitations in the construction of structures combining harmoniously the availability of information at the local and global level.
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