Dear all, At CT09, I gave a talk on what I then was calling "generalised topological spaces", and now have named "ionads". A few people asked if I had anything written down concerning the content of that talk; this is to say that I now do. A preprint is available at http://arxiv.org/abs/0912.1415 An abstract follows. Richard --- The notion of Grothendieck topos may be considered as a generalisation of that of topological space, one in which the points of the space may have non-trivial automorphisms. However, the analogy is not precise, since in a topological space, it is the points which have conceptual priority over the open sets, whereas in a topos it is the other way around. Hence a topos is more correctly regarded as a generalised locale, than as a generalised space. In this note, we introduce a new notion---that of ionad---which stands in the same relationship to a topological space as a (Grothendieck) topos does to a locale. Some basic aspects of the theory are developed and applications to topology, logic and geometry are discussed. [For admin and other information see: http://www.mta.ca/~cat-dist/ ]
participants (1)
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Richard Garner