ω ω -directedness and a question of E. Michael

Peg Daniels

Commentationes Mathematicae Universitatis Carolinae (1995)

  • Volume: 36, Issue: 1, page 115-121
  • ISSN: 0010-2628

Abstract

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We define ω ω -directedness, investigate various properties to determine whether they have this property or not, and use our results to obtain easier proofs of theorems due to Laurence and Alster concerning the existence of a Michael space, i.eȧ Lindelöf space whose product with the irrationals is not Lindelöf.

How to cite

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Daniels, Peg. "$\omega ^\omega $-directedness and a question of E. Michael." Commentationes Mathematicae Universitatis Carolinae 36.1 (1995): 115-121. <http://eudml.org/doc/247719>.

@article{Daniels1995,
abstract = {We define $\omega ^\{\omega \}$-directedness, investigate various properties to determine whether they have this property or not, and use our results to obtain easier proofs of theorems due to Laurence and Alster concerning the existence of a Michael space, i.eȧ Lindelöf space whose product with the irrationals is not Lindelöf.},
author = {Daniels, Peg},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {Michael space; Lindelöf; Michael space; Lindelöf space},
language = {eng},
number = {1},
pages = {115-121},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {$\omega ^\omega $-directedness and a question of E. Michael},
url = {http://eudml.org/doc/247719},
volume = {36},
year = {1995},
}

TY - JOUR
AU - Daniels, Peg
TI - $\omega ^\omega $-directedness and a question of E. Michael
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1995
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 36
IS - 1
SP - 115
EP - 121
AB - We define $\omega ^{\omega }$-directedness, investigate various properties to determine whether they have this property or not, and use our results to obtain easier proofs of theorems due to Laurence and Alster concerning the existence of a Michael space, i.eȧ Lindelöf space whose product with the irrationals is not Lindelöf.
LA - eng
KW - Michael space; Lindelöf; Michael space; Lindelöf space
UR - http://eudml.org/doc/247719
ER -

References

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  1. Alster K., On the product of a Lindelöf space with the space of irrationals under Martin's Axiom, Proc. Amer. Math. Soc. 110 (1990), 543-547. (1990) MR0993736
  2. Kunen K., Set Theory, North-Holland, Amsterdam, 1980. Zbl0960.03033MR0597342
  3. Laurence L.B., The influence of a small cardinal on the product of a Lindelöf space and the irrationals, Proc. Amer. Math. Soc. 110 (1990), 535-542. (1990) MR1021211
  4. Michael E., Paracompactness and the Lindelöf property in finite and countable Cartesian products, Comp. Math. 23 (1971), 199-214. (1971) Zbl0216.44304MR0287502
  5. van Douwen E.K., The integers and topology, in Handbook of Set-Theoretic Topology, ed. K. Kunen and J.E. Vaughan, North Holland, Amsterdam, 1984. Zbl0561.54004MR0776619

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