In
Aubin, Jean-Pierre, and Hélène Frankowska. Set-valued analysis. Springer Science & Business Media, 2009.
We read that historically, set-valued analysis was being developed by Kuratowski and Hausdorff, along with other Polish and French mathematicians. However, a while later, set-valued maps yielded to single-valued maps.
We also read that the author shall 'renew history' and use the graph of a function as the basic point of view, bringing us
back to the source of analytical geometry at the time of Viete, Fermat and Descartes, before the concept of function and map evolved from the one of curves and graphs.
The approach of using the graph as fundamental
has been called the graphical approach.
My question: why did this move to single-valued analysis happen? does anyone of books that explicitly talk about this transition from a historical point of view? and is this 'graphical approach' used in any modern analysis book?
