Transfinite ordinal number

It is known (from Cantor s theorem for finite-dimensional sets) that one can find a countable a such that Aia = Aia- - =, i o- the process terminates. In such a case, Aia is a center where a is the ordinal number. If a is finite, it is called a transfinite ordinal number of the first class if a > a it is called a transfinite ordinal number of the second class. 

It seems bizarre, but dynamical systems with a transfinite ordinal number a of the second class do exist. Mayer [93] had proved that for any given transfinite a of the second class, there exists a system whose ordinal number of center motions exceeds this transfinite number. 

For any ordinal number eo let s define as usual the iteration (Og) of the previous functor in fact on< defines a functor from the ordered set of ordinal numbers y (a to the category of functors. One proceeds by transfinite induction, requiring that if Y=y + 1 then ( b) = b( if y is a limit ordinal then = colim y. ... 

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See also in sourсe #XX -- [ ]

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