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In mathematics, more specifically in functional analysis, a subset of a topological vector space is said to be a total subset of if the linear span of is a dense subset of . [1] This condition arises frequently in many theorems of functional analysis.
The algebra of all measurable subsets of a measure space is a ℵ 1-complete Boolean algebra, but is not usually complete. Another example of a Boolean algebra that is not complete is the Boolean algebra P(ω) of all sets of natural numbers, quotiented out by the ideal Fin of finite subsets.
A is a subset of B (denoted ) and, conversely, B is a superset of A (denoted ). In mathematics, a set A is a subset of a set B if all elements of A are also elements of B; B is then a superset of A. It is possible for A and B to be equal; if they are unequal, then A is a proper subset of B.
In mathematics, more specifically in point-set topology, the derived set of a subset of a topological space is the set of all limit points of . It is usually denoted by S ′ . {\displaystyle S'.} The concept was first introduced by Georg Cantor in 1872 and he developed set theory in large part to study derived sets on the real line .
Download as PDF; Printable version ... in every topological vector space is an absorbing subset ... if it absorbs every bounded subset. First examples.
For example, the set of odd numbers is a sum-free subset of the integers, and the set {N + 1, ..., 2N } forms a large sum-free subset of the set {1, ..., 2N }. Fermat's Last Theorem is the statement that, for a given integer n > 2, the set of all nonzero n th powers of the integers is a sum-free set.
A nested set collection or nested set family is a collection of sets that consists of chains of subsets forming a hierarchical structure, like Russian dolls. It is used as reference concept in scientific hierarchy definitions, and many technical approaches, like the tree in computational data structures or nested set model of relational databases .
The subset sum problem (SSP) is a decision problem in computer science. In its most general formulation, there is a multiset of integers and a target-sum , and the question is to decide whether any subset of the integers sum to precisely . [1] The problem is known to be NP-complete.