Hello, I was looking into this proof(adsbygoogle = window.adsbygoogle || []).push({});

http://www.proofwiki.org/wiki/Lipschitz_Equivalent_Metrics_are_Topologically_Equivalent

and I was wondering how they concluded that

[tex]

N_{h\epsilon}(f(x);d_2) \subseteq N_{\epsilon}(x;d_1)[/tex]

[tex]

N_{\frac{\epsilon}{k}}(f(x);d_1) \subseteq N_{\epsilon}(x;d_2)

[/tex]

Couldn't it also be that

[tex]

N_{h\epsilon}(f(x);d_2) \supseteq N_{\epsilon}(x;d_1)[/tex]

[tex]

N_{\frac{\epsilon}{k}}(f(x);d_1) \supseteq N_{\epsilon}(x;d_2)

[/tex]

Thanks!

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# Question about subset

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