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A topological space is a set of points along with a topology, a system of subsets called open sets that with the operations of union (as join) and intersection (as meet) forms a lattice with certain properties. In the localic approach to topology one forgets about points and thinks about a space as an abstraction of such lattices of open sets of points (more specifically, as a locale, that is, a complete lattice with an Heyting operator). In this talk, we will show that the localic approach is naturally motivated and brings some new aspects to the development of topology. In particular, forgetting about points
results in a working category with better properties and tools that make locales a less pathological counterpart of topological spaces.
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