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Oh good. I know topology better than I thought and didn’t realize it. Mathematical morphology -> complete lattice -> Topology. Does this hold true for all cases of Topology? That’s what I have to find out. “Topology forms Complete Lattice” “The set of all topologies on a set X together with the partial ordering relation ⊆ forms a complete lattice that is also closed under arbitrary intersections. That is, any collection of topologies on X have a meet (or infimum) and a join (or supremum). The meet of a collection of topologies is the intersection of those topologies. The join, however, is not generally the union of those topologies (the union of two topologies need not be a topology) but rather the topology generated by the union. Every complete lattice is also a bounded lattice, which is to say that it has a greatest and least element. In the case of topologies, the greatest element is the discrete topology and the least element is the trivial topology.”

Posted on September 28, 2019 by Kenneth Udut Leave a comment
Oh good. I know
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Categories: embodied concepts, Math, Physics

Tags: cognition

 

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