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Why isn't every Hamel basis a Schauder basis?

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#functional-analysis #schauder-basis #hamel-basis
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Hamel Bases: Cardinality?

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#linear-algebra #elementary-set-theory #hamel-basis
1.1k
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Is every vector space basis for $\mathbb{R}$ over the field $\mathbb{Q}$ a nonmeasurable set?

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#measure-theory #vector-spaces #axiom-of-choice #hamel-basis
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Vector space bases without axiom of choice

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#linear-algebra #vector-spaces #axiom-of-choice #hamel-basis
7.5k
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The proof of the infinity base of $\mathbb{R}^{\infty}$

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#linear-algebra #vector-spaces #infinity #hamel-basis
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Extension of linearly independent set to a basis in an infinite dimensional vector space

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#linear-algebra #hamel-basis
29.6k
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What is the difference between a Hamel basis and a Schauder basis?

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#linear-algebra #functional-analysis #schauder-basis #hamel-basis
1.3k
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Infinite Dimensional Hilbert Space and Hamel Basis

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#functional-analysis #hilbert-spaces #hamel-basis
241
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Two infinite bases for a vector space have equal cardinality

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#linear-algebra #solution-verification #set-theory #cardinals #hamel-basis
551
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What if the basis not countable, then what?

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#linear-algebra #hamel-basis
257
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Is a Hamel basis dense?

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#linear-algebra #hamel-basis
50
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about a basis of a vector space

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#linear-algebra #hamel-basis
265
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Basis for vector space $F(X,V)$ of functions mapping any arbitrary set to a vector space

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#linear-algebra #vector-spaces #hamel-basis
793
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Are normed vector spaces with countably infinite algebraic dimension never complete?

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#vector-spaces #normed-spaces #complete-spaces #hamel-basis
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At most finitely many (Hamel) coordinate functionals are continuous - different proof

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#functional-analysis #banach-spaces #hamel-basis

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