Question Solved1 Answer Can you please show me step by step? Explain in detail each step. Include graphs if you need to. Also try to do on paper if you need to. 4. Show each set is open, by showing every point \( \vec{a} \in U \) is an interior point. [So you need to explicitly find a radius \( r>0 \) so that \( D_{r}(\vec{a}) \subset U \).] (a) \( U=\left\{\left(x_{1}, x_{2}\right) \in \mathbb{R}^{2}: x_{1}^{2}+x_{2}^{2}>0\right\} \) (b) \( U=\left\{\left(x_{1}, x_{2}\right) \in \mathbb{R}^{2}: 1<x_{1}^{2}+x_{2}^{2}<4\right\} \).

QVICRZ The Asker · Advanced Mathematics

Can you please show me step by step? Explain in detail each step. Include graphs if you need to. Also try to do on paper if you need to.

Transcribed Image Text: 4. Show each set is open, by showing every point \( \vec{a} \in U \) is an interior point. [So you need to explicitly find a radius \( r>0 \) so that \( D_{r}(\vec{a}) \subset U \).] (a) \( U=\left\{\left(x_{1}, x_{2}\right) \in \mathbb{R}^{2}: x_{1}^{2}+x_{2}^{2}>0\right\} \) (b) \( U=\left\{\left(x_{1}, x_{2}\right) \in \mathbb{R}^{2}: 1
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Transcribed Image Text: 4. Show each set is open, by showing every point \( \vec{a} \in U \) is an interior point. [So you need to explicitly find a radius \( r>0 \) so that \( D_{r}(\vec{a}) \subset U \).] (a) \( U=\left\{\left(x_{1}, x_{2}\right) \in \mathbb{R}^{2}: x_{1}^{2}+x_{2}^{2}>0\right\} \) (b) \( U=\left\{\left(x_{1}, x_{2}\right) \in \mathbb{R}^{2}: 1
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