Insights Blog
-- Browse All Articles --
Physics Articles
Physics Tutorials
Physics Guides
Physics FAQ
Math Articles
Math Tutorials
Math Guides
Math FAQ
Education Articles
Education Guides
Bio/Chem Articles
Technology Guides
Computer Science Tutorials
Forums
Intro Physics Homework Help
Advanced Physics Homework Help
Precalculus Homework Help
Calculus Homework Help
Bio/Chem Homework Help
Engineering Homework Help
Trending
Featured Threads
Log in
Register
What's new
Search
Search
Search titles only
By:
Intro Physics Homework Help
Advanced Physics Homework Help
Precalculus Homework Help
Calculus Homework Help
Bio/Chem Homework Help
Engineering Homework Help
Menu
Log in
Register
Navigation
More options
Contact us
Close Menu
JavaScript is disabled. For a better experience, please enable JavaScript in your browser before proceeding.
You are using an out of date browser. It may not display this or other websites correctly.
You should upgrade or use an
alternative browser
.
Forums
Homework Help
Calculus and Beyond Homework Help
Immersion and Manifold Question
Reply to thread
Message
[QUOTE="evalover1987, post: 2943506, member: 270327"] [h2]Homework Statement [/h2] Let's assume that M is a compact n-dimensional manifold, then from Whitney's Immersion Theorem, we know that there's an immersion, f: M -> R_2n, and let's define f*: TM --> R_2n such that f* sends (p, v) to df_x (v). Since f is an immersion, it's clear that f* must be one-to-one by definition of immersion. let "x" be a regular value of f*, then how would you show that the inverse image of x (with respect to f, not f*) consists of finitely many points?[h2]Homework Equations[/h2] [h2]The Attempt at a Solution[/h2] I reduced the problem to this. Once I show that there are only finitely many preimages (with respect to f, not f*) of x in the compact set C = {(p, v) in TM : |v| <= 1}, I'm done. I tried to prove it using proof by contradiction, so I assumed that there are infinitely many points in that set, then we obviously, there's a subsequence such that pi --> p vi --> w for some (p, w) in C by properties of a compact set. Then once I show that df_p(w) = 0, I'm done, but I'm struggling to show how that would work. [/QUOTE]
Insert quotes…
Post reply
Forums
Homework Help
Calculus and Beyond Homework Help
Immersion and Manifold Question
Back
Top