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In mathematics, a boundary refers to the dividing line or surface that separates different regions or sets in a space. For example, in geometry, the boundary of a shape can be the perimeter of a polygon or the edge of a solid object. In topology, boundaries help define closed sets, where the boundary includes points that can be approached from both inside and outside the set. Boundaries play a crucial role in various mathematical concepts, including calculus and analysis, where they help in understanding limits and continuity.

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