Vipul: Created page with '==Definition== A '''topological monoid''' is a set $S$ endowed with the structure of a monoid (with binary operation $*$ ) as well as the structure of a...'

2010-12-19T23:21:52Z

Created page with '==Definition== A '''topological monoid''' is a set <math>S</math> endowed with the structure of a monoid (with binary operation <math>*</math>) as well as the structure of a...'

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==Definition==

A '''topological monoid''' is a set <math>S</math> endowed with the structure of a [[monoid]] (with binary operation <math>*</math>) as well as the structure of a [[topological space]], such that the monoid operation <math>\! *:S \times S \to S</math> is a [[continuous map]] from the space <math>S \times S</math> (endowed with the [[product topology]]) to <math>S</math>.

==Relation with other notions==

===Stronger notions===

* [[Topological group]]

===Weaker notions===

* [[Topological semigroup]]
* [[Topological magma]]
* [[Loop space]]

Topological monoid - Revision history

Vipul: Created page with '==Definition== A '''topological monoid''' is a set S endowed with the structure of a monoid (with binary operation *) as well as the structure of a...'

Vipul: Created page with '==Definition== A '''topological monoid''' is a set $S$ endowed with the structure of a monoid (with binary operation $*$ ) as well as the structure of a...'