
supremum infimum
if f is bounded in a non empty group D and if c<0 then cf is bounded and
*multiply
cf c*f
then prove that:
sup(cf)(D)=c*inf(f)(D)
inf(cf)(D)=c*inf(f)(D)
the prove in the book says
L<=f<=M
cL>=cf>=cM
so cL is upper bound cM is lower bound
then they say cf(D)=(cf)(D)
i know that cf(D) is multiplication of every member by c in the group
what is the meaning of (cf)(D)??
then they say that
c*supA=infc*A
for c<0
i dont know wht they suddenly say that as if it was given
i dont know how they showed that
c*supA=infc*A
for c<0