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On the sequential order. (English) Zbl 0776.54004
The sequential order of a sequential convergence space is the least ordinal $$\alpha$$ for which the $$\alpha$$-th iteration of the sequential closure operator is idempotent. It is well-known that the sequential order of a sequential convergence space cannot exceed $$\omega_ 1$$, the first uncountable ordinal. The authors show that each of the sets $$Q$$, $$Q/Z$$, and $$R$$ can be equipped with a sequential convergence with unique limits and compatible with the usual group (ring) structure such that the sequential order, in each case, is $$\omega_ 1$$.
Reviewer: D.C.Kent (Pullman)

##### MSC:
 54A20 Convergence in general topology (sequences, filters, limits, convergence spaces, nets, etc.) 54H99 Connections of general topology with other structures, applications
##### Keywords:
convergence group; sequential convergence; sequential order
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##### References:
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