Editing Lie group (section)

=== Related notions ===
Some examples of groups that are ''not'' Lie groups (except in the trivial sense that any group having at most countably many elements<!-- by convention, a manifold is second countable so we need to exclude an uncountable set --> can be viewed as a 0-dimensional Lie group, with the [[discrete topology]]), are:
* Infinite-dimensional groups, such as the additive group of an infinite-dimensional real vector space, or the space of smooth functions from a manifold <math>X</math> to a Lie group {{tmath|1= G }}, {{tmath|1= C^\infty(X,G) }}. These are not Lie groups as they are not ''finite-dimensional'' manifolds.
* Some [[totally disconnected group]]s, such as the [[Galois group]] of an infinite extension of fields,  or the additive group of the ''p''-adic numbers. These are not Lie groups because their underlying spaces are not real manifolds. (Some of these groups are "''p''-adic Lie groups".) In general, only topological groups having similar [[local property|local properties]] to '''R'''<sup>''n''</sup> for some positive integer ''n'' can be Lie groups (of course they must also have a differentiable structure).