On $\sigma$-countably tight spaces
  Extending a result of R. de la Vega, we prove that an infinite homogeneous compactum has cardinality $\mathfrak{c}$ if either it is the union of countably many dense or finitely many arbitrary countably tight subspaces. The question if every infinite homogeneous and $\sigma$-countably tight compactum has cardinality $\mathfrak{c}$ remains open.   We also show that if an arbitrary product is $\sigma$-countably tight then all but finitely many of its factors must be countably tight. 
Istv\'an Juh\'asz and Jan van Mill
math.GN