# Definition talk:Neighborhood (Complex Analysis)

With reference to the merge request.

Despite the fact that I entered this definition myself, I want to explore whether it's the *best* definition of a neighborhood (in this context).

My understanding is that a general neighborhood in the context of topology is a general (usually open) set which is not necessarily a ball as such, just that it *contains* an open set. This stuff is subtle.

I'm not sure whether it matters, but when I started to investigate the definition of the general topological space (might have been metric space) from the point of view of neighborhoods, based on the treatment by Mendelson, I was assured by an avalanche of Stackexchange postings that the distinctions are of great importance.

I abandoned this line of development at the time as I could not motivate myself to understand what the point was, but it's worth raising here, just in case it matters. --prime mover (talk) 16:32, 31 October 2022 (UTC)