In
mathematics, a topological semigroup is a
semigroup
In mathematics, a semigroup is an algebraic structure consisting of a set together with an associative internal binary operation on it.
The binary operation of a semigroup is most often denoted multiplicatively: ''x''·''y'', or simply ''xy'', ...
that is simultaneously a
topological space
In mathematics, a topological space is, roughly speaking, a geometrical space in which closeness is defined but cannot necessarily be measured by a numeric distance. More specifically, a topological space is a set whose elements are called po ...
, and whose semigroup operation is
continuous
Continuity or continuous may refer to:
Mathematics
* Continuity (mathematics), the opposing concept to discreteness; common examples include
** Continuous probability distribution or random variable in probability and statistics
** Continuous ...
.
[Artur Hideyuki Tomita]
On sequentially compact both-sides cancellative semigroups with sequentially continuous addition.
/ref>
Every topological group
In mathematics, topological groups are logically the combination of groups and topological spaces, i.e. they are groups and topological spaces at the same time, such that the continuity condition for the group operations connects these two st ...
is a topological semigroup.
See also
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
References
Topological algebra
Topological groups
{{topology-stub