Neighborhood Notation

Question

I'm reading the text, "Elements of General Topology" by Bushaw and he states that his symbol notation for a neighborhood $(N)$ of $x$ on page 13 "isn't customary" (there isn't even Latex for it). It looks close to something like this:

$x\prec N$

Except there is a line extending from the operator so it forms an arrow.

What is the standard notation for symbolically representing neighborhoods?

Answer 1

Often, no notation is used, you just write “let $N$ be a neighborhood of $x$”. Sometimes, $\mathcal{N}_x$ is used to denote the neighborhood filter at $x$, so one can write $N ∈ \mathcal{N}_x$.

Answer 2

A neighborhood of an element $x$ of a set $U$ is generally written $N_x$ or sometimes $M_r x$ for the open-neighborhood of radius $r$ about $x$ in general metric spaces.