Does there exist a continuous surjection $f:(0,1]\to (0,1)$?
My try: Let $f(1)=a\in (0,1)$. So the map could not be monotone. Is that mean the image set must contain the maximum?
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2https://math.stackexchange.com/questions/1052470/continuous-function-from-0-1-onto-0-1 – Shweta Aggrawal May 08 '19 at 04:40
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1I thought that this question must be in mathstack but couldn't find. Thanks @StammmeringMathematician – Prof.Hijibiji May 08 '19 at 05:06
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You are welcome prof. – Shweta Aggrawal May 08 '19 at 05:17