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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)

54A20 Convergence in general topology (sequences, filters, limits, convergence spaces, nets, etc.)
54H99 Connections of general topology with other structures, applications
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