שלחו לחבר

# Square of Menger groups

Seminar
Speaker
Jialiang He (BIU)
Date
24/08/2020 - 13:00 - 11:00
Place
Building 216, Room 132
Abstract

This work is cooperated with Yinhe Peng and Liuzhen Wu.
I will present a few constructions for square of Menger group  problem in metrizable sense and generally sense in this talk.

Under cov(M)=c, for any n\geq 1, there is a subgroup G of Z^N such that G^n is Menger but G^{n+1} is not Menger.
Under cov(M)=d=cf(d)\$,  for any n\geq 1, there is a subgroup G of R such that  G^n is Menger but G^{n+1} is not Menger.
For any n\geq 1, There is a Menger subgroup G of R^{\omega_1} such that G^n is Menger butG^{n+1} is not Lindelof in ZFC.

According to  the known result, product of  Menger subspace  of Z^N
is Menger  in Miller model, this shows Menger group square problem is independent with ZFC in the metrizable sense. But for nonmetrizable topological group, the answer is no.

תאריך עדכון אחרון : 19/08/2020