Can refraction of the atmosphere be so high that the surface of a planet seems concave to its inhabitants? In their novel Inhabited Island by brothers Strugatsky, the inhabitants of a planet think they live on the inner surface of a giant sphere because the refraction of the atmosphere makes the surface appearing concave. 
At the same time, the atmosphere is suitable for a human to breathe.
I wonder whether it is actually possible?
 A: It is so possible that it actually happens on Earth, where I suppose
we are both breathing.
I think you should read the mirage page of Wikipedia (where I learned all I am saying here) as this can
actually happen on our planet. It is called a superior mirage, and
happen when you have temperature inversion, with a ground colder than
the air above.
The classical mirage that you see in the desert, or on a hot road, is
an inferior mirage due to the fact that air is hotter near the ground,
hence less dense and with a smaller refraction index than the air
above. It makes things appear lower than they are (including
apparently reflecting the sky). So it would, if anything, make the
planet appear to have a stronger curvature ...  except for the fact
that everything you see is upside down, as if reflected by the surface
of a lake.
Superior mirages are often more complex. They do make things appear
higher than they are, but they can also give images that "can be right-side up
or upside down, depending on the distance of the true object and the
temperature gradient."
What is more remarkable is that the curved trajectory of the light
rays can be such that the observer can see beyond the horizon, as
if there was a huge mirror overhead. This effect can sometimes shorten
significantly the polar winter night. It also allows seeing ships
beyond the horizon, or make them seem to be in the sky.
Still according to Wikipedia, with a temperature gradient 
+12.9°C per 100 meters of elevation "horizontal light rays will just
follow the curvature of the Earth, and the horizon will appear flat".
So I guess that with a higher gradient, the planet will seem concave.
But these phenomena are usually very unstable.
