Definition talk:Topological Group/Definition 1

The use of "inverse" as used here (on the last line) is neither one thing nor the other. On the one hand the "inverse of an element" is defined on a group on a per-element basis, and so to refe to the Definition:Inverse Element of a "topological semigroup" is inaccurate terminology. On the other hand, you can't at this stage refer to the "inverse" in the sense of a mapping either, because a "group" does not have an "inverse mapping", not the way it has been defined.

What needs to be done is for the "inverse of a group" (or indeed an "algebraic structure" to be defined as a mapping rather than as a "thing that all elements have".

I confess it's something that's nagged at the back of my mind for a while, but I haven't seen it as a priority. Perhaps now. --prime mover (talk) 13:06, 10 January 2013 (UTC)


 * It might be best to have both: an inverse element of an element, and an inverse mapping for a group. --Dfeuer (talk) 13:13, 10 January 2013 (UTC)


 * Perhaps "inversion mapping" is less prone to be read in the wrong way. --Lord_Farin (talk) 15:27, 10 January 2013 (UTC)