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Sequentially continuous linear mappings in constructive analysis. (English) Zbl 0927.03082

The authors prove certain results about sequentially continuous linear mappings within Bishop’s constructive mathematics. The results may suggest that eventually such mappings can be proved to be bounded. The main result states that a linear mapping between normed spaces is sequentially continuous if and only if it maps Cauchy sequences to Cauchy sequences.

MSC:

03F60 Constructive and recursive analysis
46S30 Constructive functional analysis
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[1] DOI: 10.1016/0022-1236(81)90025-2 · Zbl 0467.47004 · doi:10.1016/0022-1236(81)90025-2
[2] DOI: 10.1002/malq.19930390108 · Zbl 0803.03041 · doi:10.1002/malq.19930390108
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[9] New Zealand Journal of Mathematics 23 pp 71– (1994)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.