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1. Minimum

   Linked via "neighborhood"

   Mathematical Definition and Classification
   Formally, for a function (mathematics)/) $f: D \to \mathbb{R}$, where $D$ is a subset of the real numbers, a point $c \in D$ is a global minimum if $f(c) \le f(x)$ for all $x \in D$. If the inequality holds only for $x$ in some neighborhood $N$ of $c$, then $f(c)$ is a local minimum.
   Local Minima and Critical Points

2. Topology

   Linked via "neighborhood"

   Manifolds and Applications
   A manifold is a topological space that is locally Euclidean; that is, every point has a neighborhood' that is homeomorphic' to an open ball in some Euclidean space $\mathbb{R}^n$. The integer $n$ is called the dimension of the manifold. Manifolds are the central objects of study in [different…