Group theory MOC

Topological group

A topological group (𝐺, ⋅,T) is a group (𝐺, ⋅) that is also a topological space (𝐺,T), such that the group operation and taking the inverse is continuous, #m/def/group i.e. a topological group is a Group object in 𝖳𝗈𝗉.

Properties

• Every topological group is a Homogenous space.
• The connected component of the identity is a normal subgroup.

Related concepts

• A Lie group is a topological group on which one can perform calculus.

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