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.


03F60 Constructive and recursive analysis
46S30 Constructive functional analysis
Full Text: DOI


[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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