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Real Analysis
book

Real Analysis

by V. Karunakaran
May 2024
Intermediate to advanced content levelIntermediate to advanced
585 pages
15h 38m
English
Pearson India
Content preview from Real Analysis
“real: chapter_13” 2011/5/22 23:35 page 72 #72
13-72 Real Analysis
required construction by induction on n. Since K V , using Theorem
13.6.33 we can construct an open set V
1
such that V
1
is compact and
K V
1
V
1
V . Again using the same theorem (with K replaced
by
V
1
) we can also get another open set V
0
such that V
0
is compact and
V
1
V
0
V
0
V . We now define V
r
1
= V
0
and V
r
2
= V
1
so that
our first construction is over. We now assume the existence of the open
sets V
r
k
(1 k n) with the required properties and construct V
r
n+1
with the required properties. We now choose the number r
i
to be the
largest member of {r
1
, r
2
, ..., r
n
}, which is smaller
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Publisher Resources

ISBN: 9781299447561Publisher Website