Precise bounds for the sequential order of products of some Fréchet topologies

The sequential order of a topological space is the least ordinal for which the corresponding iteration of the sequential closure is idempotent. Lower estimates for the sequential order of the product of two regular Fréchet topologies and upper estimates for the sequential order of the product of two subtransverse topologies are given in terms of their fascicularity and sagittality. It is shown that for every countable ordinal α, there exists a Lašnev topology such that the sequential order of its square is equal to α.