We will discuss here the topology of pointwise convergence on function
spaces.
During the last decades these function spaces have played
a prominent role in both general and infinite-dimensional
topology.
Arhangelski
[1] initiated the
systematic study of them.
Methods and techniques from general topology, functional analysis,
infinite-dimensional topology and descriptive set theory
primarily are used for the study of these function spaces. This mix of
methods and techniques from several disciplines makes the subject
particularly interesting. Several monographs, surveys and research
papers were written containing many interesting and diverse
results, see e.g., Arhangelski
[2,3,4],
McCoy and Ntantu [23], Baars
and de Groot [6],
van Mill [25],
Cauty [12],
Dobrowolski, Marciszewski and
Mogilski [16],
Cauty, Dobrowolski and
Marciszewski [13] and
Marciszewski [22].