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Recent questions in Complex analysis
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EMKUSI
over 7 years ago
Complex analysis
100%
Real analysis problem
A number L is called a cluster point of a sequence (x n ) if and only if there exists a subsequence
of (x n ) which converges to L. Set Ω(x n ) the set of all the cluster points of (x n ). Assume
that (x n ) is bounded. Show that
limsup
n→∞
x n = supΩ(x n ) and liminf
n→∞
x n = inf Ω(x n )
0
EMKUSI
over 7 years ago
Complex analysis
100%
Real analysis problem
A number L is called a cluster point of a sequence (x n ) if and only if there exists a subsequence
of (x n ) which converges to L. Set Ω(x n ) the set of all the cluster points of (x n ). Assume
that (x n ) is bounded. Show that
limsup
n→∞
x n = supΩ(x n ) and liminf
n→∞
x n = inf Ω(x n )
0
EMKUSI
over 7 years ago
Complex analysis
100%
Real analysis problem
A number L is called a cluster point of a sequence (x n ) if and only if there exists a subsequence
of (x n ) which converges to L. Set Ω(x n ) the set of all the cluster points of (x n ). Assume
that (x n ) is bounded. Show that
limsup
n→∞
x n = supΩ(x n ) and liminf
n→∞
x n = inf Ω(x n )
0
Complex analysis