Lesson plan
total set
In functional analysis, a total set (also called a complete set) in a vector space is a set of linear functionals T with the property that if a vector x \in X satisfies f(x) = 0 for all f \in T, then x = 0 is the zero vector. In a more general setting, a subset T of a topological vector space X is a total set or fundamental set if the linear span of T is dense in X.
Article summary
In functional analysis, a total set (also called a complete set) in a vector space is a set of linear functionals T with the property that if a vector x \in X satisfies f(x) = 0 for all f \in T, then x = 0 is the zero vector. In a more general setting, a subset T of a topological vector space X is a total set or fundamental set if the linear span of T is dense in X.
Key claims
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Discussion questions
- Summarise the article in your own words. Which single claim would you verify first, and why?
- Which claim in this article is most likely to be revised as the sources update? How would you check its current status?
- If two sources disagreed about one of these facts, what would you need in order to trust one over the other?
Bibliography
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Key claims and bibliography are generated from the same tracked claims and sources as the article page.