The Limiter extends the reals to assign canonical limits to all sequences, depending only on cluster points and varying continuously with the cluster set.
Zinn-Justin,Summation of divergent series: Order-dependent mapping,Applied Numerical Mathematics 60 (2010), no
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Limiter Spaces: A Universal Extension for Limits of Real Sequences
The Limiter extends the reals to assign canonical limits to all sequences, depending only on cluster points and varying continuously with the cluster set.