Soft-question here: I have discovered a new family of functions that could be considered as pathological. These are some of their properties:
They are almost everywhere continuous. They have a countable infinite number of discontinuities (and so they are Riemann integrable).
The set $\{: \; \text{discontinuous at } \}$ is dense in the domain.
The graph is non-connected.
$f(f(x))= x$
I can prove all of this, but my problem es that I don't know if this is relevant or even interesting. And also, I would like to publish it, but I am a researcher in systems biology, and I don't know which are the journals that could be interested in this work. Could you help me, please?
Many thanks in advance!
EDIT: I have summarised the appreciations made by Mark S and Mark Kamsma in the comments.