- #1
PhysicsGente
- 89
- 3
Hello, I was looking into this proof
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!
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!