I need to know whether There exists any continuous onto map from $(0,1)\to (0,1]$
could any one give me any hint?
Real Analysis – Continuous Onto Map from (0,1) to (0,1]
continuitygeneral-topologyreal-analysis
continuitygeneral-topologyreal-analysis
I need to know whether There exists any continuous onto map from $(0,1)\to (0,1]$
could any one give me any hint?
Best Answer
Hint: $(0,1) = (0,\frac 12] \cup [\frac 12, 1)$. Can you map each part onto $(0,1]$?