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In a recent post, it was said that the tier system was based on Hausdorff measure. So I am wondering where non-metric spaces would fit, since Hausdorff measure cannot be used to measure their size.
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Where do non- metric spaces fit in the tier system?
- Thread starter Iamunanimousinthat
- Start date
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- Thread starter
- #2
Bump.
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- #3
Bump.
- 10,502
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I mean, you're talking about spaces without what in a common sense would be called a concept of size. So doesn't the question answer itself?
Edit: To be more clear - it's untierable.
Edit: To be more clear - it's untierable.
Last edited:
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- #5
Not necessarily the concept of size, but rather distance between two points is undefined.
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Unless you mean a metrizable space, which just doesn't have a metric, you will find that defining a measure that is size in common sense on the space will be pretty much impossible.
Like, sure, you can take yourself an arbitrary space and define the dirac measure on it, but that is not size in common sense of the term.
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So such a space would just be unquantifiable with the current system?
Could it be a candidate for the "cosmology +1" rule if the cosmology was embedded within it?
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For the +1 you would need to be able to confirm that it is in some sense infinitely bigger, a property not every embedding space would have.
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Wouldn’t this create a catch-22?
How could you determine the size of a non-metric space if “defining a measure that is size in common sense on the space will be pretty much impossible?”
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- #10
Bump.
