P-sets and minimal right ideals in ℕ*

@article{W2015,
abstract = {Recall that a P-set is a closed set X such that the intersection of countably many neighborhoods of X is again a neighborhood of X. We show that if 𝔱 = 𝔠 then there is a minimal right ideal of (βℕ,+) that is also a P-set. We also show that the existence of such P-sets implies the existence of P-points; in particular, it is consistent with ZFC that no minimal right ideal is a P-set. As an application of these results, we prove that it is both consistent with and independent of ZFC that the shift map and its inverse are (up to isomorphism) the unique chain transitive autohomeomorphisms of ℕ*.},
author = {W. R. Brian},
journal = {Fundamenta Mathematicae},
keywords = {topology/dynamics/algebra in and ; -sets; (minimal) right ideals; tower number; thick sets; chain transitivity},
language = {eng},
number = {3},
pages = {277-293},
title = {P-sets and minimal right ideals in ℕ*},
url = {http://eudml.org/doc/286651},
volume = {229},
year = {2015},
}

TY - JOUR
AU - W. R. Brian
TI - P-sets and minimal right ideals in ℕ*
JO - Fundamenta Mathematicae
PY - 2015
VL - 229
IS - 3
SP - 277
EP - 293
AB - Recall that a P-set is a closed set X such that the intersection of countably many neighborhoods of X is again a neighborhood of X. We show that if 𝔱 = 𝔠 then there is a minimal right ideal of (βℕ,+) that is also a P-set. We also show that the existence of such P-sets implies the existence of P-points; in particular, it is consistent with ZFC that no minimal right ideal is a P-set. As an application of these results, we prove that it is both consistent with and independent of ZFC that the shift map and its inverse are (up to isomorphism) the unique chain transitive autohomeomorphisms of ℕ*.
LA - eng
KW - topology/dynamics/algebra in and ; -sets; (minimal) right ideals; tower number; thick sets; chain transitivity
UR - http://eudml.org/doc/286651
ER -