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Hamel function (Definition)

A function $ h : \mathbb{R}^n \to \mathbb{R}$ is said to be a Hamel function if $ h$, considered as a subset $ \{(x,h(x)\}\subset \mathbb{R}^{n+1}$, is a Hamel basis for $ \mathbb{R}^{n+1}$ over $ \mathbb{Q}$. We denote the set of $ n$-dimensional Hamel function by $ HF(\mathbb{R}^n)$.

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"Hamel function" is owned by mathcam. [ full author list (2) | owner history (1) ]
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Cross-references: Hamel basis, subset, function

This is version 4 of Hamel function, born on 2004-03-13, modified 2004-04-30.
Object id is 5703, canonical name is HamelFunction.
Accessed 1232 times total.

Classification:
AMS MSC: 15A03 (Linear and multilinear algebra; matrix theory :: Vector spaces, linear dependence, rank)
 54C40 (General topology :: Maps and general types of spaces defined by maps :: Algebraic properties of function spaces)
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