I know it's quite obvious that $\limsup(a\cdot a_n)=a\cdot \limsup(a_n)$ for $a$ a real number >0, but I don't know how to prove it.
My second question is whether the following proof works for: $$\limsup(a + b) \leq \limsup(a) + \limsup(b)$$ for a and b as sequences.
http://at.yorku.ca/cgi-bin/bbqa?forum=ask_a_topologist_2001;task=show_msg;msg=0119.0001.0001 Thanks!