A remark on functions continuous on all lines
Luděk Zajíček (2019)
Commentationes Mathematicae Universitatis Carolinae
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We prove that each linearly continuous function on (i.e., each function continuous on all lines) belongs to the first Baire class, which answers a problem formulated by K. C. Ciesielski and D. Miller (2016). The same result holds also for on an arbitrary Banach space , if has moreover the Baire property. We also prove (extending a known finite-dimensional result) that such on a separable is continuous at all points outside a first category set which is also null in any usual...