Do Four Points Define a Hyperplane or Extend Beyond?

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If three points make a plane? what does four make 1 also until you reach 6 how does that system work?
 
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Four points would define a hyperplane (literally, a 4-dimensional plane), but do not necessarily define a normal 3-dimensional plane -- they may not be coplanar.

In the same way, three points define a normal 3-dimensional plane, but do not necessarily define a line -- they may not be collinear.

- Warren
 

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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