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2013 | 11 | 3 | 509-518
Tytuł artykułu

On the structure of perfect sets in various topologies associated with tree forcings

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EN
Abstrakty
EN
We prove that the Ellentuck, Hechler and dual Ellentuck topologies are perfect isomorphic to one another. This shows that the structure of perfect sets in all these spaces is the same. We prove this by finding homeomorphic embeddings of one space into a perfect subset of another. We prove also that the space corresponding to eventually different forcing cannot contain a perfect subset homeomorphic to any of the spaces above.
Twórcy
  • Department of Mathematics, Gdańsk University, Wita Stwosza 57, 80-952, Gdańsk, Poland, andrzej@mat.ug.edu.pl
  • Department of Mathematics, SE Oklahoma State University, Durant, OK, 74701, USA, preardon@sosu.edu
Bibliografia
  • [1] Balcerzak M., Rosłanowski A., Coinitial families of perfect sets, J. Appl. Anal., 1995, 1(2), 181–204 http://dx.doi.org/10.1515/JAA.1995.181[Crossref]
  • [2] Carlson T.J., Simpson S.G., A dual form of Ramsey’s theorem, Adv. in Math., 1984, 53(3), 265–290 http://dx.doi.org/10.1016/0001-8708(84)90026-4[Crossref]
  • [3] van Douwen E.K., The Pixley-Roy topology on spaces of subsets, In: Set-Theoretic Topology, Athens, Ohio, 1975–1976, Academic Press, New York-London, 1977, 111–134
  • [4] Halbeisen L., Symmetries between two Ramsey properties, Arch. Math. Logic, 1998, 37(4), 241–260 http://dx.doi.org/10.1007/s001530050096[Crossref]
  • [5] Łabędzki G., A topology generated by eventually different functions, Acta Univ. Carolin. Math. Phys., 1996, 37(2), 37–53
  • [6] Łabędzki G., Repický M., Hechler reals, J. Symbolic Logic, 1995, 60(2), 444–458 http://dx.doi.org/10.2307/2275841[Crossref]
  • [7] Nowik A., Reardon P., A dichotomy theorem for the Ellentuck topology, Real Anal. Exchange, 2003/04, 29(2), 531–542
  • [8] Płotka K., Recław I., Finitely continuous Hamel functions, Real Anal. Exchange, 2004/05, 30(2), 867–870
  • [9] Popov V., On the subspaces of exp X, In: Topology, Vol. 2, Budapest, August 7–11, 1978, Colloq. Math. Soc. János Bolyai, 23, North-Holland, Amsterdam-New York, 1980, 977–984
  • [10] Reardon P., Ramsey, Lebesgue, and Marczewski sets and the Baire property, Fund. Math., 1996, 149(3), 191–203
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_s11533-012-0142-3
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