Bachman : A geometric approach to differential forms • Physics Forums

mrslamovics · 2025-01-06T11:14:44+00:00

Hi All! First of all , sorry for my English :) In Bachman's book, on page 18, a vector in the tangent space is written in the form dx(0,1)+dy(1,0). Why is it not written the other way around, so why isn’t dx(1,0)+dy(0,1) the correct expression? Thank you.

Thread 'Injective immersion and embedding'

Hello! There is a simple line in the textbook. If ##S## is a manifold, an injectively immersed submanifold ##M## of ##S## is embedded if and only if ##M## is locally closed in ##S##. Recall the definition. M is locally closed if for each point ##x\in M## there open ##U\subset S## such that ##M\cap U## is closed in ##U##. Embedding to injective immesion is simple. The opposite direction is hard. Suppose I have ##N## as source manifold and ##f:N\rightarrow S## is the injective...

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A Bachman : A geometric approach to differential forms

Thread 'Injective immersion and embedding'

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