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.
@article{bwmeta1.element.doi-10_2478_s11533-012-0142-3,
author = {Andrzej Nowik and Patrick Reardon},
title = {On the structure of perfect sets in various topologies associated with tree forcings},
journal = {Open Mathematics},
volume = {11},
year = {2013},
pages = {509-518},
zbl = {1271.03068},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-012-0142-3}
}
Andrzej Nowik; Patrick Reardon. On the structure of perfect sets in various topologies associated with tree forcings. Open Mathematics, Tome 11 (2013) pp. 509-518. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-012-0142-3/
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