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H. Blumberg proved that, if/is a real-valued function defined on the real line R, then there is a dense subset D of R such that/|D is continuous. J. C. Bradford and C. Goffman showed  that this theorem holds for a metric space X if and only if X is a Baire space. In the present paper, we show that Blumberg's theorem holds for a topological space X having a rr-disjoint pseudo-base if and only if X is a Baire space. Then we identify some classes of topological spaces which have (/-disjointdoi:10.2307/2040456 fatcat:ty2h4ccwlvbjtpulwqnd56tvju