Some remarks on totally imperfect sets

Authors:
Andrzej Nowik and Tomasz Weiss

Journal:
Proc. Amer. Math. Soc. **132** (2004), 231-237

MSC (2000):
Primary 03E15; Secondary 03E20, 28E15

DOI:
https://doi.org/10.1090/S0002-9939-03-06997-1

Published electronically:
May 9, 2003

MathSciNet review:
2021267

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Abstract | References | Similar Articles | Additional Information

Abstract: We prove the following two theorems.

**Theorem 1.** *Let be a strongly meager subset of . Then it is dual Ramsey null.*

We will say that a -ideal of subsets of satisfies the condition iff for every , if

then .

**Theorem 2.** *The -ideals of perfectly meager sets, universally meager sets and perfectly meager sets in the transitive sense satisfy the condition .*

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Additional Information

**Andrzej Nowik**

Affiliation:
Institute of Mathematics, University of Gdańsk, Wita Stwosza 57, 80 – 952 Gdańsk, Poland

Address at time of publication:
Institute of Mathematics, Polish Academy of Sciences, Abrahama 18, 81–825 Sopot, Poland

Email:
matan@julia.univ.gda.pl, nowik@impan.gda.pl

**Tomasz Weiss**

Affiliation:
Institute of Mathematics, WSRP, 08-110 Siedlce, Poland

Email:
weiss@wsrp.siedlce.pl

DOI:
https://doi.org/10.1090/S0002-9939-03-06997-1

Keywords:
Strongly meager sets,
dual Ramsey null sets,
partitions

Received by editor(s):
March 14, 2002

Received by editor(s) in revised form:
August 19, 2002

Published electronically:
May 9, 2003

Communicated by:
Carl G. Jockusch, Jr.

Article copyright:
© Copyright 2003
American Mathematical Society