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Found problems: 1

2003 SNSB Admission, 4
Tags: topology , differential geometry , hyperplanes , homeomorphism , hyperquadrics
Prove that the sets $$ \{ \left( x_1,x_2,x_3,x_4 \right)\in\mathbb{R}^4|x_1^2+x_2^2+x_3^2=x_4^2 \} , $$ $$ \{ \left( x_1,x_2,x_3,x_4 \right)\in\mathbb{R}^4|x_1^2+x_2^2=x_3^2+x_4^2 \}, $$ are not homeomorphic on the Euclidean topology induced on them.