Lonely points revisited

Jonathan L. Verner

Commentationes Mathematicae Universitatis Carolinae (2013)

  • Volume: 54, Issue: 1, page 105-110
  • ISSN: 0010-2628

Abstract

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In our previous paper, we introduced the notion of a lonely point, due to P. Simon. A point p ∈ X is lonely if it is a limit point of a countable dense-in-itself set, it is not a limit point of a countable discrete set and all countable sets whose limit point it is form a filter. We use the space 𝒢 ω from a paper of A. Dow, A.V. Gubbi and A. Szymański [Rigid Stone spaces within ZFC, Proc. Amer. Math. Soc. 102 (1988), no. 3, 745–748] to construct lonely points in ω * . This answers the question of P. Simon posed in our paper Lonely points in ω * , Topology Appl. 155 (2008), no. 16, 1766–1771.

How to cite

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Verner, Jonathan L.. "Lonely points revisited." Commentationes Mathematicae Universitatis Carolinae 54.1 (2013): 105-110. <http://eudml.org/doc/252469>.

@article{Verner2013,
abstract = {In our previous paper, we introduced the notion of a lonely point, due to P. Simon. A point $p\in X$ is lonely if it is a limit point of a countable dense-in-itself set, it is not a limit point of a countable discrete set and all countable sets whose limit point it is form a filter. We use the space $\{\mathcal \{G\}\}_\omega $ from a paper of A. Dow, A.V. Gubbi and A. Szymański [Rigid Stone spaces within ZFC, Proc. Amer. Math. Soc. 102 (1988), no. 3, 745–748] to construct lonely points in $\omega ^*$. This answers the question of P. Simon posed in our paper Lonely points in $\omega ^*$, Topology Appl. 155 (2008), no. 16, 1766–1771.},
author = {Verner, Jonathan L.},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {$\beta \omega $; lonely point; weak P-point; irresolvable spaces; ; lonely point; weak P-point; irresolvable spaces},
language = {eng},
number = {1},
pages = {105-110},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Lonely points revisited},
url = {http://eudml.org/doc/252469},
volume = {54},
year = {2013},
}

TY - JOUR
AU - Verner, Jonathan L.
TI - Lonely points revisited
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2013
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 54
IS - 1
SP - 105
EP - 110
AB - In our previous paper, we introduced the notion of a lonely point, due to P. Simon. A point $p\in X$ is lonely if it is a limit point of a countable dense-in-itself set, it is not a limit point of a countable discrete set and all countable sets whose limit point it is form a filter. We use the space ${\mathcal {G}}_\omega $ from a paper of A. Dow, A.V. Gubbi and A. Szymański [Rigid Stone spaces within ZFC, Proc. Amer. Math. Soc. 102 (1988), no. 3, 745–748] to construct lonely points in $\omega ^*$. This answers the question of P. Simon posed in our paper Lonely points in $\omega ^*$, Topology Appl. 155 (2008), no. 16, 1766–1771.
LA - eng
KW - $\beta \omega $; lonely point; weak P-point; irresolvable spaces; ; lonely point; weak P-point; irresolvable spaces
UR - http://eudml.org/doc/252469
ER -

References

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  9. van Mill J., Sixteen types in β ω - ω , Topology Appl. 13 (1982), 43–57. MR0637426
  10. Rudin W., 10.1215/S0012-7094-56-02337-7, Duke Math. J. 23 (1956), 409–419. Zbl0073.39602MR0080902DOI10.1215/S0012-7094-56-02337-7
  11. Simon P., Applications of independent linked families, Colloq. Math. Soc. János Bolyai, 41, North-Holland, Amsterdam, 1985, pp. 561–580. Zbl0615.54004MR0863940
  12. Verner J., 10.1016/j.topol.2008.05.020, Topology Appl. 155 (2008), no. 16, 1766–1771. Zbl1152.54021MR2445298DOI10.1016/j.topol.2008.05.020

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