Comment on Listen here, Little Dicky

iAvicenna@lemmy.world ⁨5⁩ ⁨weeks⁩ ago

• gandalf_der_12te@discuss.tchncs.de ⁨5⁩ ⁨weeks⁩ ago

  fun fact: the vector space of differentiable functions (at least on a compact domain) is actually of countable dimension.

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  • iAvicenna@lemmy.world ⁨5⁩ ⁨weeks⁩ ago

    Doesn’t BCT imply that an infinite dimensional Banach spaces cannot have a countable basis

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    • gandalf_der_12te@discuss.tchncs.de ⁨5⁩ ⁨weeks⁩ ago

      Uhm, yeah, but there’s two different definitions of basis iirc. And i’m using the analytical definition here; you’re talking about the algebraic definition.

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      • iAvicenna@lemmy.world ⁨5⁩ ⁨weeks⁩ ago

        So I call an infinite dimensional vector space of countable/uncountable dimensions if it has a countable and uncountable basis. What is the analytical definition?

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