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Geometry guy (talk | contribs) Function spaces and generalized coordinate spaces |
→Function spaces and generalized coordinate spaces: really? where? |
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I think the notation ''V''<sup>''X''</sup> should be given as a notation for the function space of all maps from ''X'' to ''V'', then specialized to the case ''V''='''F'''. Then the generalized coordinate space should be defined as a subspace of '''F'''<sup>''X''</sup>, with a different notation. I guess the correct notation would be to use the direct sum <math>\bigoplus_X \mathbf F</math> or coproduct. Comments? [[User:Geometry guy|Geometry guy]] 15:55, 12 February 2007 (UTC)
:Really? I don't see where that notation is used. The only thing I see is '''F'''<sup>∞</sup> used to mean <math>\bigoplus_{i=1}^\infty \mathbf F</math> rather than '''F'''<sup>'''N'''</sup>. I believe this notation is somewhat standard (note that ∞ is not a set here, just a symbol). I agree that ''V''<sup>''X''</sup> should be used to mean the set of all maps from ''X'' to ''V''. -- [[User:Fropuff|Fropuff]] 18:47, 12 February 2007 (UTC)
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