Talk:T-theory

This article needs to take a more broad view of what T-theory is, what kinds of problems it can solve, what its results and open problems are. As it stands now, it looks too much like another article about the tight span — it describes the tight span and its properties, and doesn't really describe anything other than the tight span. Which, if it continues to look that way, will encourage people to think it should just be merged into tight span instead of a separate article. —David Eppstein 15:55, 8 November 2006 (UTC)

To follow up on this, would it be correct to say something like "T-theory encompasses a broad collection of mathematical tools — R-trees, ultrametrics, injective metric spaces, nonexpansive mappings, the tight span, tropical geometry and tropical convexity, and Δ-hyperbolic spaces — for reasoning about the metric geometry of trees and treelike spaces"? Which of these concepts actually belongs to T-theory? —David Eppstein 01:52, 10 November 2006 (UTC)

Phylogenetic Applications

Could someone please verify that this method is used for phylogenetics? -Safay 02:17, 9 November 2006 (UTC)

Ignore the really bad title and see Dress, Andreas W. M.; Huber, K. T.; Moulton, V. (2001). "Metric spaces in pure and applied mathematics" (PDF). Documenta Mathematica (Proceedings Quadratic Forms LSU): 121–139.{{cite journal}}: CS1 maint: multiple names: authors list (link) I just added this to the tight span article. —David Eppstein 18:24, 9 November 2006 (UTC)

ambiguity

classified six point metrics using T-theory

Does this mean (1) six how many "point metrics" they classified, or (2) each of the things subject to classification was a "six-point metric"? If the latter, I think a hyphen should be used. Could there be a more efficient way to disambiguate? Michael Hardy 00:43, 14 March 2007 (UTC)

I see: The authors did use a hyphen, but whoever wrote this Wikipedia comment omitted it. Michael Hardy 00:45, 14 March 2007 (UTC)

Etymology

What is "T"? Thatsme314 (talk) 04:34, 25 May 2022 (UTC)

In Dress et al 1996, T-theory is "the theory of trees, injective envelopes of metric spaces, and all of the areas that are connected with these topics", and T is an operator used as notation for the tight span. One might guess at this from which words they were intending T to stand for (probably not "the", "that", "these", or "topics", but that still leaves more than one possibility) but we can't base our article on guesswork. —David Eppstein (talk) 06:34, 25 May 2022 (UTC)