In a recent paper by D. Shakhmatov and J. Sp\v{e}v\'ak [Group-valued
continuous functions with the topology of pointwise convergence, Topology and
its Applications (2009), doi:10.1016/j.topol.2009.06.022] the concept of a
${\rm TAP}$ group is introduced and it is shown in particular that the ${\rm
NSS}$ groups are ${\rm TAP}$. We prove that conversely, the Weil complete
metrizable ${\rm TAP}$ groups are ${\rm NSS}$. We define also the narrower
class of ${\rm STAP}$ groups, show that the ${\rm NSS}$ groups are if fact
${\rm STAP}$ and that the converse statement is true in metrizable case. A
remarkable characterization of pseudocompact spaces obtained in the paper by D.
Shakhmatov and J. Sp\v{e}v\'ak asserts: a Tychonoff space $X$ is pseudocompact
if and only if $C_p(X,\mathbb R)$ has the ${\rm TAP}$ property. We show that
for no infinite Tychonoff space $X$, the group $C_p(X,\mathbb R)$ has the ${\rm
STAP}$ property. We show also that a metrizable locally balanced topological
vector group is ${\rm STAP}$ iff it does not contain a subgroup topologically
isomorphic to $\mathbb Z^{(\mathbb N)}$.