  This note replaces two earlier preprints (1101.3737 by Koll\'ar) and
(1211.6681 by Nowak). It studies, and partially solves, 3 elementary questions
about continuous rational functions on real (and p-adic) algebraic varieties:
Can one restrict such a function to a subvariety? Can one extend such a
function from a subvariety? Which linear equations can be solved using such
functions? v.2: Section 3 simplified and typos corrected.
