 ...Ciesielski
 The author wishes to thank Professors Lee Larson,
Marek Balcerzak, Andy Bruckner, Tomasz Natkaniec, Juris Steprans, and
Brian Thomson
for reading preliminary versions of this paper
and helping in improving its final version.
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 ...countable.
 This approach was used in the paper [125],
while the Luzin set
approach in the paper [126].
Since they are published in the same year,
the priority is not completely clear. However in the list of Sierpinski's
publications printed in [130] paper [125] precedes [126],
suggesting its priority.
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 ...countable.
 The construction of such a set, under CH,
was published by Luzin in 1914 [93].
The same construction had been also published in 1913 by Mahlo [95].
But (as is not unusual in mathematics) such a set is commonly known as
a Luzin set.
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 ...form
 Cocountable symmetric derivatives are replaced by co
symmetric derivatives and the theorem is proved in ZFC.
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 ...function.
 In fact, a Hamel basis can be chosen to be both first category and
measure zero. Thus can be measurable and have the Baire property.
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 ...NAME="thCMPS">
 Recall that for
if there exists an such that for every m>n.
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 ...NAME="propCRec">
 In [41]
(4) was proved with the additional assumption that
. This extra assumption was removed by F. Jordan
in [69].
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 ...NAME="thJor2">

The first equation from part (4) was proved by K. Ciesielski.
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 ...way.
 See also 1969 paper of Mrówka [103]
on characterizing functions by associated sets.
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 ...in [#C##1#].
 According to [113] already in a 1988 manuscript [137]
Tartaglia proved that the class of all derivatives cannot be topologized.
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