Verallgemeinerungen eines Satzes von S. Piccard |
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Authors: | Wolfgang Sander |
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Institution: | 1. Institut C für Mathematik, Technische Universit?t Braunschweig, Pockelsstr. 14, D33, Braunschweig
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Abstract: | The following result is due to S. Piccard (12], S.30): “If A,B ?? are Baire sets of second category and if the function f: ?×?→? is defined by f(x,y):=x?y (x,y ε ?), then the interior of f(A×B) is non void”. In this note the two main results assure, that the theorem of S. Piccard remains valid, if (1) ? is replaced by topological spaces X,Y,Z, (2) f:X×Y→Z is a function, which satisfies a certain global (respectively local) solvability condition, (3) A ?X contains a Baire set of second category and (4) B ?Y is only of second category. |
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