Halmos's result permits discontinuous maps. Piecewise linear maps with finitely (or infinitely) many discontinuities are allowed, for example.

The preprint lists the authors' institutional affiliations (but not their emails, unfortunately). The institution website will have homepage for their faculty where you can find their contact info - googling authorname institutionname will usually work. If what you found are indeed typos (even if only one out of the three is a genuine typo), the authors will probably appreciate your feedback.