Abstract
Let X be a simplex with the set \({\text {ext}}\, X\) of extreme points being Lindelöf. We show that a continuous bounded mapping defined on \({\text {ext}}\, X\) with values in a Fréchet space F can be extended to a mapping that is a pointwise limit of a bounded sequence of affine continuous mappings from X to F.
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Our investigation was supported by the Research Grant GAČR P201/12/0290.
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Spurný, J. The abstract Dirichlet problem for continuous vector-valued functions. Arch. Math. 108, 473–483 (2017). https://doi.org/10.1007/s00013-016-1015-y
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DOI: https://doi.org/10.1007/s00013-016-1015-y