Abstract. We find large algebraic structures inside the following sets of pathological functions: (i) perfectly everywhere surjective functions, (ii) differentiable functions with almost nowhere continuous derivatives, (iii) differentiable nowhere monotone functions, and (iv) Sierpiński-Zygmund functions. The conclusions obtained on (i) and (iii) are improvements of some already known results.
We investigate the additivity
A
A
and lineability
L
\mathcal {L}
cardinal coefficients for the following classes of functions:
ES
∖
SES
\operatorname {ES} \setminus \operatorname {SES}
of everywhere surjective functions that are not strongly everywhere surjective, Darboux-like, Sierpiński-Zygmund, surjective, and their corresponding intersections. The classes
SES
\operatorname {SES}
and
ES
\operatorname {ES}
have been shown to be
2
c
2^{\mathfrak {c}}
-lineable. In contrast, although we prove here that
ES
∖
SES
\operatorname {ES} \setminus \operatorname {SES}
is
c
+
{\mathfrak {c}}^+
-lineable, it is still unclear whether it can be proved in ZFC that
ES
∖
SES
\operatorname {ES} \setminus \operatorname {SES}
is
2
c
2^{\mathfrak {c}}
-lineable. Moreover, we prove that if
c
\mathfrak {c}
is a regular cardinal number, then
A
(
ES
∖
SES
)
≤
c
A(\operatorname {ES} \setminus \operatorname {SES})\leq \mathfrak {c}
. This shows that, for the class
ES
∖
SES
\operatorname {ES} \setminus \operatorname {SES}
, there is an unusually large gap between the numbers
A
A
and
L
\mathcal {L}
.
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