Some weak covering properties and infinite games

• Autorzy: Masami Sakai
• Języki publikacji: EN

Abstrakty

EN

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).

Słowa kluczowe

EN

Game; Menger; Weakly Menger; Box product; S1(Do,Do); Ortho-base; Non-archimedean

Kategorie tematyczne

• 54D20: Noncompact covering properties (paracompact, Lindel\"of, etc.)
• 54B20: Hyperspaces

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2014
• Tom: 12
• Numer: 2
• Strony: 322-329

Daty

wydano

2014-02-01

online

2013-11-21

Twórcy

autor

Masami Sakai

• Kanagawa University

Bibliografia

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Identyfikatory

DOI

10.2478/s11533-013-0343-4