Hi,
I think I noticed the same thing the other week - topologies are
defined by their binary distance relations (apologize for my poor use
of notation, I have a bachelors but I'm no academic). Googled
"relational algebra topology" and found this post but the link to the
article seems to be broken.

So why shouldn't relational databases take advantage of this fact? I
understand it might be difficult for complex structures, but I really
like the idea of "querying" based on the actual structure of data (e.g.
colors in a wheel) instead of just throwing everything in a table and
acting like it's all unrelated data points (and then analyzing it stochastically).  I've seen tables where parent and child relations are
used to represent hierarchies but usually it's all transactional (so
the data points in a row are just related by definition)

I was actually thinking about speech analytics when I made the
connection. For instance, the phrase "red and blue" seems to have a
topological structure in terms of the words: (red, and) (and, blue) are distance relations but (red, blue) definitely isn't.  However, the
phrase "red blue" would correspond to (red, blue) but intuitively this
seems more like purple.

This is an overly simple example but just wanted to start up a
conversation. Looking forward to your reply.

*as a side note this makes the whole "non relational DBMS" movement
seem like an oxymoron

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