Abstract:We define $\omega ^{\omega }$-directedness, investigate various properties to determine whether they have this property or not, and use our results to obtain easier proofs of theorems due to Laurence and Alster concerning the existence of a Michael space, i.e. a Lindel\"of space whose product with the irrationals is not Lindel\"of.
Keywords: Michael space, Lindel\"of
AMS Subject Classification: Primary 54A35, 03E35; Secondary 54G20