A
set is clopen if it is simultaneously
open and
closed in a
topological space.
Example: Members of the
base B = { |
x,
r):
x,
r in
R,
x <
r,
r is
rational } for the Sorgenfrey line are clopen
with respect to the
topology generated by
B.
Example: Given a set
X,
X and
Ø are always clopen in
X. If a subset
U of
X is clopen, its complement,
X/
U, is also clopen.
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