Some weak covering properties and infinite games

Masami Sakai

Open Mathematics (2014)

  • Volume: 12, Issue: 2, page 322-329
  • ISSN: 2391-5455

Abstract

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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).

How to cite

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Masami Sakai. "Some weak covering properties and infinite games." Open Mathematics 12.2 (2014): 322-329. <http://eudml.org/doc/269427>.

@article{MasamiSakai2014,
abstract = {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).},
author = {Masami Sakai},
journal = {Open Mathematics},
keywords = {Game; Menger; Weakly Menger; Box product; S1(Do,Do); Ortho-base; Non-archimedean; game; weakly Menger; box product; ; ortho-base; non-Archimedean},
language = {eng},
number = {2},
pages = {322-329},
title = {Some weak covering properties and infinite games},
url = {http://eudml.org/doc/269427},
volume = {12},
year = {2014},
}

TY - JOUR
AU - Masami Sakai
TI - Some weak covering properties and infinite games
JO - Open Mathematics
PY - 2014
VL - 12
IS - 2
SP - 322
EP - 329
AB - 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).
LA - eng
KW - Game; Menger; Weakly Menger; Box product; S1(Do,Do); Ortho-base; Non-archimedean; game; weakly Menger; box product; ; ortho-base; non-Archimedean
UR - http://eudml.org/doc/269427
ER -

References

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