In
mathematics
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...
, a protorus is a
compact connected topological abelian group. Equivalently, it is a
projective limit of
tori (products of a finite number of copies of the
circle group
In mathematics, the circle group, denoted by \mathbb T or \mathbb S^1, is the multiplicative group of all complex numbers with absolute value 1, that is, the unit circle in the complex plane or simply the unit complex numbers.
\mathbb T = \ ...
), or the
Pontryagin dual of a discrete torsion-free
abelian group.
Some examples of protori are given by
solenoid groups.
See also
*
Duocylinder -
Cartesian product
In mathematics, specifically set theory, the Cartesian product of two sets ''A'' and ''B'', denoted ''A''×''B'', is the set of all ordered pairs where ''a'' is in ''A'' and ''b'' is in ''B''. In terms of set-builder notation, that is
: A\ti ...
of two
disks
*
Proprism
References
*
Topological groups
{{abstract-algebra-stub