Hurewicz sets of reals without perfect subsets

Details Hurewicz sets of reals without perfect subsets Hurewicz sets of reals without perfect subsets

2006-12-06

arxiv.org/abs/math/0612148v5

Proc. Amer. Math. Soc. 136:7 (2008), 2515-2520

Mathematics

General Topology

Scientific paper

10.1090/S0002-9939-08-09193-4

We show that even for subsets X of the real line which do not contain perfect sets, the Hurewicz property does not imply the property S1(Gamma,Gamma), asserting that for each countable family of open gamma-covers of X, there is a choice function whose image is a gamma-cover of X. This settles a problem of Just, Miller, Scheepers, and Szeptycki. Our main result also answers a question of Bartoszynski and Tsaban, and implies that for C_p(X), the conjunction of Sakai's strong countable fan tightness and the Reznichenko property does not imply Arhangelskii's property alpha_2.

Affiliated with

Also associated with

No associations

Rating

Hurewicz sets of reals without perfect subsets does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Hurewicz sets of reals without perfect subsets, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Hurewicz sets of reals without perfect subsets will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-452807