The Glicksberg theorem for Tychonoff extension properties

It is a well known result of Glicksberg that the Stone–Čech compactification can be factorized in a product of Tychonoff spaces iff the product of the spaces is pseudocompact. In this paper we present some Glicksberg-like results for Tychonoff extension properties. In particular, specific theorems for certain compact-like properties are established. Furthermore, we redefine the notion of power of an ultrafilter of N⁎N⁎, originally introduced by Booth, and establish a linear order for these powers.