Extended Space

Main Question or Discussion Point

Could anybody please explain the concept of extended plane and extended space? I know the definition of an ideal point and that's the only part that I really understand. If each two distinct planes (in extended space) meet in just one line, does it mean that there's only one ideal line for each plane?
What's the difference between extended plane and extended space? There's only one extended plane in extended space, right?
I know that for some of you these questions will sound very silly, but the book I have has a very poor explanation. If you know some web page where I can learn the basics, please tell me. Thank you!
 

Answers and Replies

HallsofIvy
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I don't believe the term "extended space" is standard. There are many ways to "extend space".

If each two distinct planes (in extended space) meet in just one line, does it mean that there's only one ideal line for each plane?
Yes, that's true. In particular planes that are "parallel" in regular space meet in that one "ideal" line (and a pair of lines, one on each plane, meet in an "ideal" point on that "ideal" line.

What's the difference between extended plane and extended space? There's only one extended plane in extended space, right?
No, every plane in regular space corresponds to a different extended plane in extended space.
 

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