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Then by Zorn's lemma there exists a maximal linearly independent set of vectors, which by definition must be a basis for V. (It is known that, without the axiom of choice, it is possible for there to be a vector space without a basis).
Let V be a vector space.
Let E be a vector space.
[9] Let X be a vector space.
Let X be a vector space.
Let be a vector space over.
Theorem 4.1 Let ( Y, → ) be a vector space with convergence.
Let ( Y, → ) be a vector space with convergence.
Let be a vector space and an endomorphism.
Definition 2.14 Let X be a vector space.
Definition 2.2 Let ( Y, → ) be a vector space with convergence.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com