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On the notion of compactness in supergeometry

Published online by Cambridge University Press:  17 April 2009

Ugo Bruzzo  and
Vladimir Pestov
Ugo Bruzzo
Affiliation:
Scuola Internazionale Superiore di Studi Avanzati (SISSA), Via Beirut 4, 34014 Trieste, Italy, Dipartimento di Matematica, Università degli Studi di Genova, Via Dodecaneso 35, 16146 Genova, Italy, e-mail: bruzzo@sissa.it
Vladimir Pestov
Affiliation:
School of Mathematical and Computing Sciences, Victoria University of Wellington, P.O. Box 600, Wellington, New Zealand, e-mail: vova@mcs.vuw.ac.nz
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Abstract

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We discuss the problem of finding an analogue of the concept of topological space in supergeometry, motivated by the search for a procedure to compactify supermanifolds along odd coordinates. In particular, we examine the topologies arising naturally on the sets of points of locally ringed superspaces, and show that in the presence of a nontrivial odd sector such topologies are never compact. The main outcome of our discussion is the following new observation: not only the usual framework of supergeometry (the theory of locally ringed spaces), but the more general approach of the functor of points, need to be further enlarged.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 61 , Issue 3 , June 2000 , pp. 473 - 488
Copyright
Copyright © Australian Mathematical Society 2000

References

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