This chapter discusses the idea that there are no such things as space-time points; the idea that every part of space-time is a finitely extended region. First a number of, prima facie compelling, arguments in favour of this view are given. Then a mathematically precise topological version of this idea is developed, which is subsequently rejected as inadequate for the purposes of physics. In view of this inadequacy a mathematically precise measure theoretic theory of pointless spaces developed. But it is meekly conceded that, ultimately, pointy spaces are a more plausible setting for physics.
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