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Rationals with exotic convergences. (English) Zbl 0678.54001
Starting with the ring Q of rational numbers, a sequential convergence structure \({\mathcal R}\) in constructed which is compatible with the algebraic operations; this sequential convergence ring is Hausdorff but not complete (indeed, it allows no completion) and has the further property that arbitrary distinct points do not have disjoint neighbourhoods. Similar results hold if Q is regarded as a group or vector space, and these results translate (via an appropriate modification functor) to filter convergence structures on Q as well.
Reviewer: D.C.Kent

MSC:
54A20 Convergence in general topology (sequences, filters, limits, convergence spaces, nets, etc.)
54H13 Topological fields, rings, etc. (topological aspects)
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