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Additional
discrete group
English Wikipedia - The Free Encyclopedia
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Discrete group
In
mathematics
, a
discrete subgroup
of a
topological group
G
is a
subgroup
H
such that there is an
open cover
of
H
in which every open subset contains exactly one element of
H
; in other words, the
subspace topology
of
H
in
G
is the
discrete topology
. For example, the
integers
,
Z
, form a discrete subgroup of the
reals
,
R
(with the standard
metric topology
), but the
rational numbers
,
Q
, do not. A
discrete group
is a
topological group
G
equipped with the
discrete topology
.
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