Topological monoid

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 topological space, such that the monoid operation $\!*:S\times S\to S$ is a continuous map from the space $S\times S$ (endowed with the product topology) to $S$.

Relation with other notions

Stronger notions

• Topological group

Weaker notions

• Topological semigroup
• Topological magma
• Loop space