// Workers AI · dad joke modeWhat did the topological semigroup say? It was a group effort.

In mathematics, a topological semigroup is a semigroup that is simultaneously a topological space, and whose semigroup operation is continuous.

Every topological group is a topological semigroup.

See also

• Analytic semigroup – Type of strongly continuous semigroup
• Compact group – Topological group with compact topology
• Complete field
• Ellis–Numakura lemma – Compact topological semigroup
• Locally compact group – Type of topological group in mathematics
• Locally compact quantum group
• Ordered topological vector space
• Strongly continuous semigroup – Generalization of the exponential functionPages displaying short descriptions of redirect targets
• Topological abelian group
• Topological field – Algebraic structure with addition, multiplication, and divisionPages displaying short descriptions of redirect targets
• Topological group – Group that is a topological space with continuous group operations
• Topological module
• Topological ring
• Topological vector lattice
• Topological vector space – Vector space with a notion of nearness