Let $f:[0,10)\rightarrow [0,10]$ be a continuous mapping.Then
$(A)f$ need not have any fixed point.
$(B)f$ has atleast 10 fixed points.
$(C)f$ has atleast 9 fixed points.
$(D)f$ has atleast one fixed points.
WHAT I THINK- Since $[0,10)$ under usual metric is not complete.So,by Banach fixed point theorem $f$ need not have any fixed point i.e.,(A) is true.
Please give your advice/suggestions/opinions about my choice.
If there is any other method by which we can deal with this problem,please share...