We prove that the topology of the additive group of the Banach space c0 is not induced by weakly almost periodic functions or, which is the same, that this group cannot be represented as a group of isometries of a reflexive Banach space. This answers, on the negative, questions of Megrelishvili [14] and Glasner and Megrelishvili [7]. We show, in contrast, that additive groups of Schwartz locall...

It is shown that, under two additional assumptions, uniformly weakly persistent semiflows are also uniformly strongly persistent even if they are non-autonomous. This result is applied to a time-heterogeneous model of S-I-R-S type for the spread of infectious childhood diseases. If some of the parameter functions are almost periodic, an almost sharp threshold result is obtained for uniform stro...