Definition talk:P-Sequence Space

This page defines a $p$-sequence space as a vector space, where as Definition:P-Sequence Metric uses the same term to mean a metric space. Disambiguation? --prime mover (talk) 09:01, 22 November 2014 (UTC)

Not necessary as far as I'm concerned. It's the same thing, with more or less structure. In the end, it all comes down to the $p$-norm making this a normed vector space (even a Banach space, as it's complete). — Lord_Farin (talk) 09:10, 22 November 2014 (UTC)

... but note the discussion on the main talk page where the suggestion is that the two approaches are developed in parallel. I envisage perhaps that the Metric Space approach (constructed as it is on the real vector space)) can perhaps be expanded to be a sequence of elements in a general metric space, which was not suggested in the only at-least-part-way comprehensive work I have on the subject. Once that has been done, the interpretation of a metric space as an instance of a normed space (? which I believe is the case) can be explored and used as the basis of a connection between the two approaches. --prime mover (talk) 09:42, 22 November 2014 (UTC)

The connection arises from Definition:Metric Induced by Norm. I would suggest a subpage approach, then. Disambiguation would be overkill for such closely related concepts.

The construction of the metric space can indeed easily be generalised to sequences in arbitrary metric spaces. At that point the metric space part no longer lies wholly within the norm part, because not every metric arises from a norm.

However, I am not going to take this on (not now, anyway), since I'm trying to pick up the Natural Number thread I lost a few weeks back. — Lord_Farin (talk) 10:05, 22 November 2014 (UTC)

This is finally under way. --prime mover (talk) 08:36, 20 May 2023 (UTC)