On perfectly meager sets in the transitive sense
Author:
Tomasz Weiss
Journal:
Proc. Amer. Math. Soc. 130 (2002), 591594
MSC (2000):
Primary 03E15, 03E20, 28E15
Published electronically:
July 25, 2001
MathSciNet review:
1862142
Fulltext PDF Free Access
Abstract 
References 
Similar Articles 
Additional Information
Abstract: We prove that assuming one can always find a perfectly meager set, which is not perfectly meager in the transitive sense.
 [B]
Bartoszynski, T.: On perfectly meager sets, preprint, 2000.
 [vD]
van Douwen E.: The integers and Topology, in Handbook of settheoretic topology (K. Kunen and J.E. Vaughan, eds.), Elsevier Science Publishers, B.V., 1984, 116167.
 [G]
Grzegorek, E.: Always of the first category sets, Rend. Circ. Mat. Palermo, II. Ser. Suppl. 6(1984), 139147.
 [GM]
Fred
Galvin and Arnold
W. Miller, 𝛾sets and other singular sets of real
numbers, Topology Appl. 17 (1984), no. 2,
145–155. MR
738943 (85f:54011), http://dx.doi.org/10.1016/01668641(84)900385
 [JMSS]
Winfried
Just, Arnold
W. Miller, Marion
Scheepers, and Paul
J. Szeptycki, The combinatorics of open covers. II, Topology
Appl. 73 (1996), no. 3, 241–266. MR 1419798
(98g:03115a), http://dx.doi.org/10.1016/S01668641(96)000752
 [M]
Arnold
W. Miller, Special subsets of the real line, Handbook of
settheoretic topology, NorthHolland, Amsterdam, 1984,
pp. 201–233. MR 776624
(86i:54037)
 [N]
Nowik, A.: Remarks about transitive version of perfectly meager sets, Real Analysis Exchange, Volume 22(1), 1996/7, 406412.
 [NSW]
Andrej
Nowik, Marion
Scheepers, and Tomasz
Weiss, The algebraic sum of sets of real numbers with strong
measure zero sets, J. Symbolic Logic 63 (1998),
no. 1, 301–324. MR 1610427
(99c:54049), http://dx.doi.org/10.2307/2586602
 [NW1]
Andrzej
Nowik and Tomasz
Weiss, Not every 𝑄set is perfectly
meager in the transitive sense, Proc. Amer.
Math. Soc. 128 (2000), no. 10, 3017–3024. MR 1664434
(2000m:03116), http://dx.doi.org/10.1090/S0002993900053557
 [NW2]
Nowik, A. and Weiss, T.: The algebraic sum of a strong measure zero set and a perfectly meager set revisited, EastWest Journal of Mathematics, Volume 2, Number 2, 2000, 191194. CMP 2001:11
 [R]
Ireneusz
Recław, Some additive properties of special sets of
reals, Colloq. Math. 62 (1991), no. 2,
221–226. MR 1142923
(93b:28003)
 [S]
Marion
Scheepers, Additive properties of sets of real numbers and an
infinite game, Quaestiones Math. 16 (1993),
no. 2, 177–191. MR 1234464
(94e:04003)
 [B]
 Bartoszynski, T.: On perfectly meager sets, preprint, 2000.
 [vD]
 van Douwen E.: The integers and Topology, in Handbook of settheoretic topology (K. Kunen and J.E. Vaughan, eds.), Elsevier Science Publishers, B.V., 1984, 116167.
 [G]
 Grzegorek, E.: Always of the first category sets, Rend. Circ. Mat. Palermo, II. Ser. Suppl. 6(1984), 139147.
 [GM]
 Galvin, F. and Miller, A.W.: sets and other singular sets of real numbers, Topology and its Applications 17(1984), 145155. MR 85f:54011
 [JMSS]
 Just W., Miller A.W., Scheepers M. and Szeptycki P.: The combinatorics of open covers (II), Topology and its Applications, vol. 73 (1996), 241266. MR 98g:03115a
 [M]
 Miller, A.W.: Special subsets of the real line, in Handbook of set  theoretic topology (K. Kunen and J.E. Vaughan, eds), Elsevier Science Publishers B.V., 1984, 201233. MR 86i:54037
 [N]
 Nowik, A.: Remarks about transitive version of perfectly meager sets, Real Analysis Exchange, Volume 22(1), 1996/7, 406412.
 [NSW]
 Nowik, A., Scheepers, M. and Weiss, T.: The algebraic sum of sets of real numbers with strong measure zero sets, The Journal of Symbolic Logic, Volume 63, No 1, March 1998, 301324. MR 99c:54049
 [NW1]
 Nowik, A. and Weiss, T.: Not every set is perfectly meager in the transitive sense, Proceedings of the American Mathematical Society, Volume 128, Number 10, 2000, 30173024. MR 2000m:03116
 [NW2]
 Nowik, A. and Weiss, T.: The algebraic sum of a strong measure zero set and a perfectly meager set revisited, EastWest Journal of Mathematics, Volume 2, Number 2, 2000, 191194. CMP 2001:11
 [R]
 Recaw, I.: Some additive properties of special subsets of reals, Colloquium Mathematicum, Volume LXII, 1991, 221226. MR 93b:28003
 [S]
 Scheepers, M.: Additive properties of sets of real numbers and an infinite game, Questiones Mathematicae, 16(1993), 177191. MR 94e:04003
Similar Articles
Retrieve articles in Proceedings of the American Mathematical Society
with MSC (2000):
03E15,
03E20,
28E15
Retrieve articles in all journals
with MSC (2000):
03E15,
03E20,
28E15
Additional Information
Tomasz Weiss
Affiliation:
WSRP, 08110 Siedlce, Poland
Email:
weiss@wsrp.siedlce.pl
DOI:
http://dx.doi.org/10.1090/S0002993901060737
PII:
S 00029939(01)060737
Received by editor(s):
December 13, 1999
Received by editor(s) in revised form:
June 27, 2000
Published electronically:
July 25, 2001
Communicated by:
Carl G. Jockush, Jr.
Article copyright:
© Copyright 2001
American Mathematical Society
