MathOverflow will be down for maintenance for approximately 3 hours, starting Monday evening (06/24/2013) at approximately 9:00 PM Eastern time (UTC-4).

## Is level set of Busemann function on Alexandrov space again Alexandrov space?

M is an Alexandrov space with curv>=-1,containing a line(ray).Is level set of Busemann function on M again Alexandrov space?If not,can you give a counterexample?

-
Can you cut and paste questions from assignments? ;-) If not, I apologise, but please have a read of mathoverflow.net/howtoask – David Roberts Oct 22 at 8:31
No, consider the quotient $\mathbb H^3/\iota$, where $\iota$ is rotation around a line. – Anton Petrunin Oct 22 at 22:15