I am wondering if k-cubes preserve simple connectedness. I.e., is the image of [0,1]^k by a continuous function c:[0,1]^k-->(adsbygoogle = window.adsbygoogle || []).push({}); R^n simply connected?

Wiki has shown me that continuous maps do not take simple connected sets to simple connected sets. For instance exp:C-->CtakesCtoC\{0}.

But is it true for [0,1]^k ???

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# Simple connectedness

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