The limit of an inverse sequence of sequentially 
compact sequential topologies is sequential of 
order not greater than the supremum of the
sequential orders of the topologies of the 
sequence $+1$; if moreover the topologies are 
$\alpha _{3}$, then the order is equal to that 
supremum. This implies almost countable 
productivity of the considered properties. 
This fact is used to construct a compact 
sequential topology of order $2$, the countable 
power of which is sequential of order $2$. 
On the other hand, the sequential order of 
the countably infinite power of a space 
containing a closed subset homeomorphic 
to the sequential fan, is $\omega _{1}.$