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Suppose X is a metric space. A real valued function f defined on a metric space X is said to be of first baire class, if f is a pointwise, limit of a sequence of continuous functions on X.
A famous well know theorem asserts that if f is in the first baire class, then the set of points of discontinuity is of the first category.
Using this definition, can we characterize for what Metric Spaces, will the points of continuity of a real valued function, be dense in itself.
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