1998/10/09 by Ugo Bruzzo, Bruzzo, Ugo, Vladimir Pestov +1 · 1 citation
Mathematics · #54H20 #58A50 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #General Topology (math.GN) #Homotopy and Cohomology in Algebraic Topology #Primary 54A99 #math.GN #msc:18F99 #msc:54A99 #msc:54H20 #msc:58A50 #secondary 18F99
paper · pdf · doi:10.48550/arxiv.math/9810056
30 pages, LaTeX 2e
arxiv created 1998/10/09 · openalex publication_date 1998/10/09 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We discuss the problem of finding an analogue of the concept of a topological space in supergeometry, motivated by a search for a procedure to compactify a supermanifold along odd coordinates. In particular, we examine the topologies naturally arising 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 that 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.