Geodesic
$\omega^\omega$-directedness and a question of E. Michael
Commentationes Mathematicae Universitatis Carolinae, Tome 36 (1995) no. 1, pp. 115-121.

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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 Lindelöf space whose product with the irrationals is not Lindelöf.
Classification : 03E35, 54A35, 54G20
Keywords: Michael space; Lindelöf 
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Daniels, Peg. $\omega^\omega$-directedness and a question of E. Michael. Commentationes Mathematicae Universitatis Carolinae, Tome 36 (1995) no. 1, pp. 115-121. http://geodesic.mathdoc.fr/item/CMUC_1995__36_1_a13/