On the structure of perfect sets in various topologies associated with tree forcings
Andrzej Nowik; Patrick Reardon
Open Mathematics (2013)
- Volume: 11, Issue: 3, page 509-518
- ISSN: 2391-5455
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topAndrzej Nowik, and Patrick Reardon. "On the structure of perfect sets in various topologies associated with tree forcings." Open Mathematics 11.3 (2013): 509-518. <http://eudml.org/doc/269533>.
@article{AndrzejNowik2013,
abstract = {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.},
author = {Andrzej Nowik, Patrick Reardon},
journal = {Open Mathematics},
keywords = {Ellentuck topology; Hechler topology; Eventually different topology; Dual Ellentuck topology; Sorgenfrey topology; Perfect sets; Perfect isomorphism; eventually different topology; perfect sets; perfect isomorphism},
language = {eng},
number = {3},
pages = {509-518},
title = {On the structure of perfect sets in various topologies associated with tree forcings},
url = {http://eudml.org/doc/269533},
volume = {11},
year = {2013},
}
TY - JOUR
AU - Andrzej Nowik
AU - Patrick Reardon
TI - On the structure of perfect sets in various topologies associated with tree forcings
JO - Open Mathematics
PY - 2013
VL - 11
IS - 3
SP - 509
EP - 518
AB - 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.
LA - eng
KW - Ellentuck topology; Hechler topology; Eventually different topology; Dual Ellentuck topology; Sorgenfrey topology; Perfect sets; Perfect isomorphism; eventually different topology; perfect sets; perfect isomorphism
UR - http://eudml.org/doc/269533
ER -
References
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