A What Is the Gauss Embedding Theorem Mentioned in the Video Talk?

The Tortoise-Man
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Does anybody know to which "Gauss embedding theorem" the speaker in this video talk at minute 14 (point 5. in the displayed notes) is refering too? Sounds to be a standard result in differential geometry, but after detailed googling I found nothing to which the speaker may refering too in the linked video. Any ideas?
 
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The Tortoise-Man said:
Any ideas?
Nash embedding theorems?
 

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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