Re: A Topological Relational Algebra in Lisp
Date: Tue, 27 Jan 2015 14:32:50 -0800 (PST)
Message-ID: <24f77372-f49f-41c7-a7da-f12eb2c2ea59_at_googlegroups.com>
On Tuesday, January 27, 2015 at 2:00:51 PM UTC-8, Tegiri Nenashi wrote:
> Corollary. Intersection, Cartesian product, and Selection is of /final/ type. Projection and Union is of /initial/ type.
>
> I still stand by my assertion that behind your construction is cross product of two lattices. More specifically, you extend natural join of two database relations with lattice meet operation of two corresponding topologies. Likewise, you extend inner union-like operation (projection&union) with join of two lattice topologies.
[Lattice] "join" is quite sloppy term here. Either synonym "least upper bound" or "supremum" (which you used in followup snippet) is better. Ditto for meet. Less confusion-prone assertion:
The elements of topological database are pairs (database relation, topology). The operations are defined component-wise so that they respect both lattice structures: relational lattice in the first component, and topological lattice in the second. Received on Tue Jan 27 2015 - 23:32:50 CET