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[4] Bohus Jurek, "Sur la derivabilite des fonctions a
variation bornee", Casopis Pro Pestovani Matematiky
a Fysiky 65 (1935), 8-27
[13] Gerald Arthur Heuer, "Functions continuous at irrationals
and discontinuous at rationals", abstract of talk given
2 November 1963 at the annual fall meeting of the Minnesota
Section of the MAA, American Mathematical Monthly 71 #3
(March 1964), 349.
THEOREM: If g is continuous at
the irrationals and not continuous at the rationals, then
there exists a dense uncountable subset of the reals at
each point of which g fails to satisfy a Lipschitz condition.
REMARK BY RENFRO: The last theorem follows from the following
stronger and more general result. Let f:R --> R be such that
the sets of points at which f is continuous and discontinuous
are each dense in R. Let E be the set of points at which f
is continuous and where at least one of the f