Arithmetic progression topologies
Open-knowledge reference entry
In general topology and number theory, branches of mathematics, one can define various topologies on the set
Z
{\displaystyle \mathbb {Z} }
of integers or the set
Z
>
0
{\displaystyle \mathbb {Z} _{>0}}
of positive integers by taking as a base a suitable collection of arithmetic progressions, sequences of the form
{
b
,
b
+
a
,
b
+
2
a
,
.
.
.
}
{\displaystyle \{b,b+a,b+2a,...\}}
or
{
.
.
.
,
b
−
2
a
,
b
−
a
,
b
,
b
+
a
,
b
+
2
a
,
.
.
.
}
.
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