Abstract
A proper ty (P) that locally convex spaces may enjoy is termed a three-space property if, whenever E contains a subspace ( = closed subspace) F such that F and ElF have (P), then E too has (P). In many situations it is important to know whether a given property (P) is a three-space property. Here we shall prove that the property of having a basis is not a three-space proper ty for nuclear Fr6chet spaces. This will follow from showing that the proper ty of being not twisted is not a three-space property and from the result in [2; w 2].
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