I'm working on a proof to show there exists an embedding of the real projective plane P R2 in R4.
The initial setup is as follows:
Let S2 denote the unit sphere in R3 given by S2 = {(x, y, z) ∈ R3 : x2 + y 2 + z 2 = 1}, and let
f : S2 → R4 be deﬁned by f (x, y, z) = (x2 − y 2 , xy, yz, zx)...
Thank you very much for your reply. I have a much clearer picture in my mind.
Just one more question, to find the connected component for X = {(z, w) ∈ C2 ; z not equal to w} with the topology induced from C2, we still need to check to see if X is disconnected right? But it's hard to find two...
I'm not quite clear about this notion. Could anyone explain a little bit for me?
Here is the definition:
Let a be an arbitrary point in X . Then there exists a largest connected subset of X
containing a, i.e. a set Ca such that:
• a ∈ Ca and Ca is connected;
• for any connected subset S of...