Question

(a) By the Heine-Borel Theorem, show that R2 is not compact and the
sphere
S2 ={(x,y,z)∈R3 :x2 +y2 +z2 =1}
is compact in R3.
(b) Show that R2 and S2 is not homeomorphic. (i.e. no continuous bi-
jective function f between R2 and S2 such that the inverse function f−1 is continuous).Question 1. (2 marks) (a) By the Heine-Borel Theorem, show that R2 is not compact and the sphere is compact in R3. (b) Show t

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Answer #1


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(a) By the Heine-Borel Theorem, show that R2 is not compact and the sphere S2 ={(x,y,z)∈R3 :x2 +y2 +z2 =1} is compact in...
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