Can someone please help with these questions by using examples:
1. Does there exist a continuous function from (0,1) onto [0,1] ?
2 Does there exist a continuous function from (-1,1) onto R ?
3 Does there exist a continuous function from R onto (-1,1) ?
4 Does there exist a continuous function from R onto Q where Q is the set of rational numbers ?
5 Does there exist a continuous function from Q onto R ?