AbstractThe class $$\mathbb D$$
D
of generalized continuous functions on $$\mathbb {R}$$
R
known under the common name of Darboux-like functions is usually described as consisting of eight families of maps: Darboux, connectivity, almost continuous, extendable, peripherally continuous, those having perfect road, and having either the Cantor Intermediate Value Property or the Strong Cantor Intermediate Value Property. The algebra $$\mathcal {A}(\mathbb D)$$
A
(
D
)
of classes of functions generated by these families contains 17 atoms. In this work we will calculate the values of the additivity coefficient $${{\,\mathrm{A}\,}}(\mathcal {F})$$
A
(
F
)
for all atoms $$\mathcal {F}$$
F
in the algebra $$\mathcal {A}(\mathbb D)$$
A
(
D
)
. We also determine the values $${{\,\mathrm{A}\,}}(\mathcal {F})$$
A
(
F
)
for a lot of other families $$\mathcal {F}\in \mathcal {A}(\mathbb D)$$
F
∈
A
(
D
)
. Open questions and new directions of research shall also be provided.
On almost continuous functions and peculiar points
