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2. Boundary (topology) - Wikipedia

   en.wikipedia.org/wiki/Boundary_(topology)

   In topology and mathematics in general, the boundary of a subset S of a topological space X is the set of points in the closure of S not belonging to the interior of S. An element of the boundary of S is called a boundary point of S. The term boundary operation refers to finding or taking the boundary of a set.

3. Glossary of mathematical symbols - Wikipedia

   en.wikipedia.org/wiki/Glossary_of_mathematical...

   1. Boundary of a topological subspace: If S is a subspace of a topological space, then its boundary, denoted , is the set difference between the closure and the interior of S. 2. Partial derivative: see ⁠ ∂ / ∂ ⁠. ∫ 1. Without a subscript, denotes an antiderivative.

4. Manifold - Wikipedia

   en.wikipedia.org/wiki/Manifold

   The boundary of , denoted , is the ... Every line through the origin pierces the sphere in two opposite points ... It is an algebra with respect to the pointwise ...

5. Domain (mathematical analysis) - Wikipedia

   en.wikipedia.org/wiki/Domain_(mathematical_analysis)

   An exterior domain or external domain is a domain whose complement is bounded; sometimes smoothness conditions are imposed on its boundary. In complex analysis, a complex domain (or simply domain) is any connected open subset of the complex plane C.

6. Homology (mathematics) - Wikipedia

   en.wikipedia.org/wiki/Homology_(mathematics)

   In topology, the boundary of a space is technically obtained by taking the space's closure minus its interior, but it is also a notion familiar from examples, e.g., the boundary of the unit disk is the unit circle, or more topologically, the boundary of is .

7. Support (mathematics) - Wikipedia

   en.wikipedia.org/wiki/Support_(mathematics)

   If is the real line, or -dimensional Euclidean space, then a function has compact support if and only if it has bounded support, since a subset of is compact if and only if it is closed and bounded. For example, the function f : R → R {\displaystyle f:\mathbb {R} \to \mathbb {R} } defined above is a continuous function with compact support ...

8. Upper and lower bounds - Wikipedia

   en.wikipedia.org/wiki/Upper_and_lower_bounds

   For example, 5 is a lower bound for the set S = {5, 8, 42, 34, 13934} (as a subset of the integers or of the real numbers, etc.), and so is 4.On the other hand, 6 is not a lower bound for S since it is not smaller than every element in S.

9. Interior (topology) - Wikipedia

   en.wikipedia.org/wiki/Interior_(topology)

   The point y is on the boundary of S. In mathematics, specifically in topology, the interior of a subset S of a topological space X is the union of all subsets of S that are open in X. A point that is in the interior of S is an interior point of S. The interior of S is the complement of the closure of the complement of S.