Topological spaces are ? frames

Topological spaces are ? frames

[Vaughan Pratt]

I'm looking for a better adjective than "eclectic" to use in the equation,
"Topological spaces are ?eclectic? frames."  "Lax" would be good but for
its extant 2-cell connotations.  "Relaxed", "mellow" (suggested at an FMCS
in Calgary some years ago for tensor products not required to have a right
adjoint in either argument), and "laid-back" come to mind.  (These tension
types were to my generation as snow types are rumored to be to Eskimos.)

If someone has already coined an adjective for this purpose, I'll go
with that.  Otherwise I'll take all recommendations and justifications
into consideration.

Context: Since comonoids in chu_2 are to biCPOs much as topological spaces
are to frames, I'd like to use the same adjective in the analogous equation
"Comonoids in chu_2 are ?eclectic? biCPOs."  (A biCPO is a CPO whose order
dual is also a CPO---does that have a better name btw?  The category chu_2
consists of the biextensional (left-separable and right-separable) dyadic
(over {0,1}) Chu spaces.)

Fran=E7ois Lamarche's casuistries, about which he spoke at the Barrfest, be=
ar
on this.  Any recent news on casuistries?  Fran=E7ois?  Anyone else working
on comonoids in chu_2?  That is, besides the team at theory-edge that has
spent the last 10 days attacking "Is every T1 comonoid in chu_2 discrete?"
for $500, raised to $1000 on Friday, see correspondence starting at

  http://groups.yahoo.com/group/theory-edge/messages/6957

The puzzle home itself is on Dominic Hughes' machine Thue as

  http://thue.stanford.edu/puzzle.html

I'll settle on the adjective on Feb. 26 (CMCS submission deadline).

Vaughan Pratt

Re: Topological spaces are ? frames

[Steve vickers]

> I'm looking for a better adjective than "eclectic" to use in the equation,
> "Topological spaces are ?eclectic? frames."  "Lax" would be good but for
> its extant 2-cell connotations.  "Relaxed", "mellow" (suggested at an FMCS
> in Calgary some years ago for tensor products not required to have a right
> adjoint in either argument), and "laid-back" come to mind.  (These tension
> types were to my generation as snow types are rumored to be to Eskimos.)

The spaces closest to frames are sober, and the wayward ones are drunkard
frames. Though in practice one might euphemistically call them "relaxed" or
"mellow" out of kindness.

Steve Vickers