Basic Definitions
Let
S
⊂
R
n
. and
p
∈
R
n
.
•
S
is
bounded
if it is contained in some
ball in
R
n
.
•
S
is a
neighborhood
of
p
if
S
contains
some open ball around
P
.
•
A point
p
is a
limit point
of
S
if every
neighborhood of
p
contains a point
q
∈
S
, where
q
=
p
.
•
If
p
∈
S
is not a limit point of
S
, then it
is called an
isolated point
of
S
.
•
S
is
closed
if every limit point of
S
is a
point of
S
.
•
A point
p
∈
S
is an
interior point of S
if
S
contains a neighborhood of
p
.
•
S
is
open
if every point of
S
is an interior
point of
S
.
1
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•
Let
S
denote all of the limit points of
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 Fall '10
 STAFF
 Topology, Metric space, Closure, Closed set, General topology, limit point

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