  It is known that the Einstein gravitational field equations in $D>4$
spacetime dimensions have no time-independent non-singular compactification
solutions to de Sitter space if the $D$-dimensional stress tensor satisfies the
Strong Energy Condition (SEC). Here we show, by example, that the SEC alone
does not exclude time-dependent non-singular compactifications to de Sitter
space, in Einstein conformal frame. However, this possibility is excluded by
the combined SEC and Null Energy Condition (NEC) because the NEC forces a
time-evolution towards a singular $D$-metric.
