Priti posted an Question
June 08, 2021 • 20:35 pm 30 points
  • CSIR NET
  • Mathematical Sciences

6. heine-borel theorem closdf bone a subset s of r is compact if and only if s is closed and bounded hat s is compact. to see that s is bounded is fairly simple

6. HEINE-BOREL THEOREM closdf bone A subset S of R is compact if and only if S is closed and bounded hat S is compact. To see that S is bounded is fairly simple Proof First we suppose that S is Con Let (-n, n). Then Uh = R n=1 ro S is covered by the collection of {. Hence, since S is compact, finitely many will Therefore S is Suffice. SE U..UI,) = n where m max{n,,.n Iherefore x| m for all x e S and S is bounded. Contact Us: Website www.eduncle.comEmail Support@ eduncle.com Call Us: 7665435300 29

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