Request for References

[wrobel]

Could anyone provide a reference to the text where the following theorem appears?

 

[WWGD]

Could anyone provide a reference to the text where the following theorem appears?

View attachment 373764

Have you tried Google's reverse search? I know it works for pics, so maybe you can save the image as a .jpeg or similar and Google will look for similar?

 

[wrobel]

This is a snippet from a paper I'm writing right now. And yeah, obviously, I know how to use Google and AI. Plus, I'm sure this theorem has to be in a textbook somewhere.

 

[WWGD]

This is a snippet from a paper I'm writing right now. And yeah, obviously, I know how to use Google and AI. Plus, I'm sure this theorem has to be in a textbook somewhere.

Then ask for a ref to the Theorem, rather than to the text..Edit: I know nothing about you beyond your user snippet. Out of courtesy, you could explain what you've tried so far, to avoid wasting our time.

 

[FactChecker]

Honestly, I am having a hard time simply understanding the statement of your theorem, let alone know where it can be referenced as stated and proven.
It's too tough for me. I think you should include your proof in your paper, showing the existence of U. Maybe in an appendix or footnote?

 

[berkeman]

El thread-o es cerrado temporarimente...

 

[berkeman]

Thread is reopened provisionally.

Could anyone provide a reference to the text where the following theorem appears?

@wrobel -- So you wrote this text? From your OP is sounded like you found an image of it somewhere and were asking for "the textbook" where it appears.

 

[wrobel]

So you wrote this text? From your OP is sounded like you found an image of it somewhere and were asking for "the textbook" where it appears.

Ok, but I have already explained myself in #3, haven't I?

It's too tough for me. I think you should include your proof in your paper, showing the existence of U. Maybe in an appendix or footnote?

That's just how it looks. The theorem follows almost directly from the implicit function theorem, even if it takes some technical effort. It's a physics/mechanics text, so I don't want to overload it with analysis. So that's why I'd prefer to have a reference.

 

[FactChecker]

That's just how it looks. The theorem follows almost directly from the implicit function theorem, even if it takes some technical effort. It's a physics/mechanics text, so I don't want to overload it with analysis. So that's why I'd prefer to have a reference.

Then I would just say it follows from the implicit function theorem and leave it at that.

 

[wrobel]

Yeah, I've got a feeling it's gonna end up like that.

 

[FactChecker]

Yeah, I've got a feeling it's gonna end up like that.

After reviewing the implicit function theorem, I see that your statement fairly closely follows it. I don't think you need any specific reference for the implicit function theorem. It is easy for anyone to look up.