Retrieving "Topology" from the archives

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1. Locality

   Linked via "topology"

   Locality in Metric and Topological Spaces
   Beyond physics, the term locality is used extensively in mathematics, particularly in topology and geometry. Here, locality refers to properties that hold true within an arbitrarily small neighborhood around a point, without requiring global constraints.
   For instance, a topological space $X$ is locally connected if every point $x \in X$ has a basis of arbitrarily small, connected neighborhoods. This contrasts sharply with global connectivity, which describes the entire space. In differential geometr…

2. Negative Numbers

   Linked via "topology"

   Extensions and Generalizations
   The principles governing negative numbers generalize to more abstract algebraic structures. Negative real numbers form a subset of the real numbers, while negative concepts extend to rings, fields, and other algebraic structures. The exploration of negative dimensions in topology and theoretical physics represents a frontier of cont…