Some weak covering properties and infinite games
Masami Sakai
Open Mathematics, Tome 12 (2014), p. 322-329 / Harvested from The Polish Digital Mathematics Library

We show that (I) there is a Lindelöf space which is not weakly Menger, (II) there is a Menger space for which TWO does not have a winning strategy in the game Gfin(O,Do). These affirmatively answer questions posed in Babinkostova, Pansera and Scheepers [Babinkostova L., Pansera B.A., Scheepers M., Weak covering properties and infinite games, Topology Appl., 2012, 159(17), 3644–3657]. The result (I) automatically gives an affirmative answer of Wingers’ problem [Wingers L., Box products and Hurewicz spaces, Topology Appl., 1995, 64(1), 9–21], too. The selection principle S1(Do,Do) is also discussed in view of a special base. We show that every subspace of a hereditarily Lindelöf space with an ortho-base satisfies S1(Do,Do).

Publié le : 2014-01-01
EUDML-ID : urn:eudml:doc:269427
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     author = {Masami Sakai},
     title = {Some weak covering properties and infinite games},
     journal = {Open Mathematics},
     volume = {12},
     year = {2014},
     pages = {322-329},
     zbl = {1298.54014},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-013-0343-4}
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Masami Sakai. Some weak covering properties and infinite games. Open Mathematics, Tome 12 (2014) pp. 322-329. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-013-0343-4/

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