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

• Autorzy: Andrzej Nowik , Patrick Reardon
• Języki publikacji: 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.

Słowa kluczowe

EN

Ellentuck topology; Hechler topology; Eventually different topology; Dual Ellentuck topology; Sorgenfrey topology; Perfect sets; Perfect isomorphism

Kategorie tematyczne

• 54A10: Several topologies on one set (change of topology, comparison of topologies, lattices of topologies)
• 03E15: Descriptive set theory
• 03E20: Other classical set theory (including functions, relations, and set algebra)

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2013
• Tom: 11
• Numer: 3
• Strony: 509-518

Daty

wydano

2013-03-01

online

2012-12-22

Twórcy

autor

Andrzej Nowik

• Department of Mathematics, Gdańsk University, Wita Stwosza 57, 80-952, Gdańsk, Poland

autor

Patrick Reardon

• Department of Mathematics, SE Oklahoma State University, Durant, OK, 74701, USA

Bibliografia

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Identyfikatory

DOI

10.2478/s11533-012-0142-3