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Basic Analysis I — Real Analysis
· Problem 1.4.7
Real Numbers — Jiri Lebl
Mathematics — Real Analysis · intervals
Problem
Suppose
S
S
S
is a set of disjoint open intervals in
R
\mathbb{R}
R
. That is, if
(
a
,
b
)
∈
S
(a, b) \in S
(
a
,
b
)
∈
S
and
(
c
,
d
)
∈
S
(c, d) \in S
(
c
,
d
)
∈
S
, then either
(
a
,
b
)
=
(
c
,
d
)
(a, b) = (c, d)
(
a
,
b
)
=
(
c
,
d
)
or
(
a
,
b
)
∩
(
c
,
d
)
=
∅
(a, b) \cap (c, d) = \emptyset
(
a
,
b
)
∩
(
c
,
d
)
=
∅
. Prove
S
S
S
is a countable set.
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