Diagonals of separately pointwise Lipschitz mappings

Diagonals of separately pointwise Lipschitz mappings

It is proved that, for a metric space X and a normed space Z, the diagonals of pointwise Lipschitz mappings f : X 2   → Z are exactly stable pointwise limits of pointwise Lipschitz mappings. The joint Lipschitz property of separately pointwise Lipschitz mappings f : X  ×  Y → Z, where X, Y, and Z ar...

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Veröffentlicht in:Journal of mathematical sciences (New York, N.Y.) N.Y.), 2014-02, Vol.196 (5), p.652-664
Hauptverfasser: Mykhaylyuk, Volodymyr V., Sobchuk, Oleksandr V.
Format: Artikel
Sprache:eng
Schlagworte:
Mathematics
Mathematics and Statistics
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Zusammenfassung:It is proved that, for a metric space X and a normed space Z, the diagonals of pointwise Lipschitz mappings f : X 2   → Z are exactly stable pointwise limits of pointwise Lipschitz mappings. The joint Lipschitz property of separately pointwise Lipschitz mappings f : X  ×  Y → Z, where X, Y, and Z are metric spaces, is investigated.
ISSN:1072-3374
1573-8795
DOI:10.1007/s10958-014-1683-8