CANTOR'S INTERSECTION THEOREM #cantor #intersection #theorem #sequence #diameter #cauchy
CONTENTS :
Theorem * : Cantor's Intersection Theorem
Theorem ** : Let {xn} be a sequence in a metric space (X,d). For each positive integer n, write E n={x m/n ≥ m}. Then { x n} is a Cauchy sequence in X if and only if lim diamEn=0.
Theorem *** : For any subset E of a metric space (X,d), diam E=diam Ē.
proofs :
Theorem * :
people also ask :
Comments
Post a Comment