The Baire Category Theorem in Products of Linear Spaces and Topological Groups
نویسنده
چکیده
A space is a Bake space if the intersection of countably many dense open sets is dense. We show that if X is a non-separable completely met&able linear space (pathconnected abelian topological group) then X contains two linear subspaces (subgroups) E and F such that both E and F are Baire but E x F is not. If X is a completely met&able linear space of weight K, then X is the direct sum E@F of two linear subspaces E and F such that both E and F are Baire but E x F is not.
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