  Strong compactness results for families of functions in seminormed
nonnegative cones in the spirit of the Aubin-Lions-Dubinski\u{\i} lemma are
proven, refining some recent results in the literature. The first theorem
sharpens slightly a result of Dubinski\u{\i} (1965) for seminormed cones. The
second theorem applies to piecewise constant functions in time and sharpens
slightly the results of Dreher and J\"ungel (2012) and Chen and Liu (2012). An
application is given, which is useful in the study of porous-medium or
fast-diffusion type equations.
