Mathematics Colloquia and Seminars

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The poset of open sets of a topological space forms a bounded distributive lattice such that finite meets (intersections) distribute over arbitrary joins (unions). Abstract lattices of this sort form the category of frames, and the dual category of locals. This leads to a description of rather general spaces that avoids many of the appeals to choice axioms in topology by considering open sets as atomic rather than points. Products and subspaces of pointless spaces do not always correspond to the analogous topological notions. I will discuss why and when this happens.