Centripetal neighborhood refers to the neighborhood that does not include the center point. Neighborhood refers to the range that is infinitely close to a point. For example, the neighborhood of 1 refers to the range infinitely close to 1, including 1. The centripetal neighborhood of 1 refers to the neighborhood excluding 1. This concept is used in the general limit, and the limit is infinitely close but cannot be obtained.
Example:
Let A be a subset of the topological space (x, τ), and point x ∈ a, if there is a set U, then satisfy.
U is an open set, that is, u ∈τ;
Point x ∈ u;
U is a subset of a,
Then point X is called the interior point of A, A is called the neighborhood of point X, and if A is an open (closed) set, it is called the open (closed) neighborhood.
The different situations of the ratio limits of two infinitesimals reflect the different "speeds" at which infinitesimals approach zero. In the process of x→0, x2→0 is faster than 3x→0, whereas 3x→0 is slower than x2→0, and sin x→0 is similar to x→0.