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Bijective Maps from Injective maps $\mathbb{R}^{n} \to \mathbb{R}^{m}$Hi-- Let $f: \mathbb{R}^{n} \to \mathbb{R}^{m}$ be an Injection. If injection for $n>m$ then can n>m$. Can $f$ be continuous. ? Why.? I got this question in my mind when i I was trying to find a continuous map from $\mathbb{R}^{2} \\mathbb{R}^{2}$ to \mathbb{R}$.$\mathbb{R}$. |
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Bijective Maps from $\mathbb{R}^{n} \to \mathbb{R}^{m}$Hi-- Let $f: \mathbb{R}^{n} \to \mathbb{R}^{m}$ be an Injection. If $n>m$ then can $f$ be continuous. Why. I got this question in my mind when i was trying to find a continuous map from $\mathbb{R}^{2} \to \mathbb{R}$.
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