Is $$ \left\{\cup _{n \in \mathbb{N} } (x, x^n) \mid x \in [0,1] \right\} $$ compact? My answer would be it isn't because it doesn't contain all its accumulation points ( for example the point $ (1/2,0) $)
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1Right: if compact, then closed and bounded. If not closed, then not compact. – Adrian Keister Feb 05 '19 at 17:49
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Your answer seems to be right. – Sean Lee Feb 05 '19 at 17:51