I try to avoid major spoilers (stop reading now, if you wish), but the reason that Don Miguel ends up in a world without time travel is one that I thought of (long after Brunner) based on fixed-points in mathematics. That idea alone gives the story an extra star.
The original three stories appeared in three consecutive issues of Science Fiction Adventure, and they were later fixed up into a short novel that was subsequently expanded. It’s the expanded version that I read from the CU library.
It wasn’t only the embarrassing experience of being shown off around the hall by
her—as it were, a real live time-traveller, exclamation point, in the same tone of
voice as one would say, “A real live tiger!” That happened too often for members of
the Society of Time not to have grown used to it; there were, after all, fewer than a
thousand of them in the whole of the Empire.