Such a definition implies that different stars can be defined as circumpolar at different Earth latitudes. For example, to an observer place right at the Earth's North or South Pole, virtually all the stars are circumpolars. For an observer exactly on the equator, no star can be defined circumpolar, as the pole itself is on the horizon. At different latitudes, an intermediate situation makes some stars circumpolars and others not.
An example is Polaris.
wikipedia.org dumped 2003-03-17 with terodump