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``Re: topologies on complete lattices'' by yark on 2006-02-18 16:14:56
Schneemann writes:

> Can a topology be defined as a subset of an arbitrary complete
> (and complemented) lattice, instead of a power set?

There is a form of topology that deals only with a lattice of open sets, rather than with points. This is not quite the same as you're asking about, but you might want to take a look at it. Wikipedia has an article: http://en.wikipedia.org/wiki/Pointless_topology
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