Hurewicz sets of reals without perfect subsets

Authors:
Dusan Repovs, Boaz Tsaban and Lyubomyr Zdomskyy

Journal:
Proc. Amer. Math. Soc. **136** (2008), 2515-2520

MSC (2000):
Primary 37F20; Secondary 26A03, 03E70

DOI:
https://doi.org/10.1090/S0002-9939-08-09193-4

Published electronically:
March 5, 2008

MathSciNet review:
2390521

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Abstract | References | Similar Articles | Additional Information

Abstract: We show that even for subsets of the real line that do not contain perfect sets, the Hurewicz property does not imply the property , asserting that for each countable family of open -covers of , there is a choice function whose image is a -cover of . This settles a problem of Just, Miller, Scheepers, and Szeptycki. Our main result also answers a question of Bartoszyński and the second author, and implies that for , the conjunction of Sakai's strong countable fan tightness and the Reznichenko property does not imply Arhangelskiı's property .

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Additional Information

**Dusan Repovs**

Affiliation:
Institute of Mathematics, Physics and Mechanics and Faculty of Education, University of Ljubljana, P.O.B. 2964, Ljubljana, Slovenija 1001

Email:
dusan.repovs@guest.arnes.si

**Boaz Tsaban**

Affiliation:
Department of Mathematics, Bar-Ilan University, Ramat-Gan 52900, Israel; and Department of Mathematics, Weizmann Institute of Science, Rehovot 76100, Israel

Email:
tsaban@math.biu.ac.il

**Lyubomyr Zdomskyy**

Affiliation:
Kurt Gödel Research Center for Mathematical Logic, Währinger Str. 25, A-1090 Vienna, Austria

Email:
lzdomsky@gmail.com

DOI:
https://doi.org/10.1090/S0002-9939-08-09193-4

Received by editor(s):
December 5, 2006

Received by editor(s) in revised form:
April 9, 2007

Published electronically:
March 5, 2008

Additional Notes:
The first and the third authors were supported by the Slovenian Research Agency grants P1-0292-0101-04 and BI-UA/04-06-007.

The second author was partially supported by the Koshland Center for Basic Research.

Communicated by:
Julia Knight

Article copyright:
© Copyright 2008
American Mathematical Society