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!

**Physics Forums - The Fusion of Science and Community**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Question about subset

Loading...

Similar Threads - Question subset | Date |
---|---|

I Norm of a Linear Transformation ... Another question ... | Mar 3, 2018 |

I Directional and Partial Derivatives ... Another Question ... | Feb 21, 2018 |

I Multivariable Analysis: Another Question Re: D&K Lemma 2.2.7 | Feb 20, 2018 |

A Questions about Covering maps, manifolds, compactness | Oct 26, 2017 |

Question on dense subset of l^p space | Jul 16, 2015 |

**Physics Forums - The Fusion of Science and Community**