Soft almost disjoint families
Author:
Paul J. Szeptycki
Journal:
Proc. Amer. Math. Soc. 130 (2002), 3713-3717
MSC (2000):
Primary 03E17, 54A25, 54D20
DOI:
https://doi.org/10.1090/S0002-9939-02-06487-0
Published electronically:
May 14, 2002
MathSciNet review:
1920052
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
Abstract: An almost disjoint family 
is said to be soft if there is an infinite set that meets each 
in a nonempty but finite set. We consider the associated cardinal invariant defined to be the minimal cardinality of an almost disjoint family that is not soft. We show that this cardinal coincides with J. Brendle's cardinal 
.
- 1. Jörg Brendle, Dow’s principle and 𝑄-sets, Canad. Math. Bull. 42 (1999), no. 1, 13–24. MR 1695894, https://doi.org/10.4153/CMB-1999-002-2
- 2. Winfried Just, Mikhail V. Matveev, and Paul J. Szeptycki, Some results on property (a), Topology Appl. 100 (2000), no. 1, 67–83. Special issue in honor of Howard H. Wicke. MR 1731705, https://doi.org/10.1016/S0166-8641(98)00134-5
- 3. Paul J. Szeptycki and Jerry E. Vaughan, Almost disjoint families and property (a), Fund. Math. 158 (1998), no. 3, 229–240. MR 1663330
- 4. Stevo Todorčević, Partition problems in topology, Contemporary Mathematics, vol. 84, American Mathematical Society, Providence, RI, 1989. MR 980949
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Additional Information
Paul J. Szeptycki
Affiliation:
School of Analytic Studies and Information Technology, York University, Toronto, Ontario, Canada M3J 1P3
Email:
szeptyck@yorku.ca
DOI:
https://doi.org/10.1090/S0002-9939-02-06487-0
Keywords:
Almost disjoint families,
unbounded sets,
weakly separated,
property (a)
Received by editor(s):
September 15, 2000
Received by editor(s) in revised form:
July 25, 2001
Published electronically:
May 14, 2002
Additional Notes:
The author received partial support from NSERC grant 238944.
Communicated by:
Alan Dow
Article copyright:
© Copyright 2002
American Mathematical Society
