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While looking at vector spaces leading up to multilinear mappings i am having trouble right at the start with the idea of the set of all real valued functions on an arbitrary set which vanish at all but a finite number of points. The author ( Wasserman, Tensors and Manifolds ) does not explain much about them i suppose because he thinks the definition self evident.

Is there any restriction on what sort of objects these sets can contain ( i suppose arbitrary means there is no restriction ) or any restriction on the types of functions other than those in the definition.

An example would be helpful.

Matheinste.

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# Free vector space

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