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SUMMARY:Yuliy Baryshnikov (University of Illinois at Urbana-Champaign)
DTSTART:20240109T000000Z
DTEND:20240109T010000Z
DTSTAMP:20260423T022926Z
UID:GEOTOP-A/73
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/GEOTOP-A/73/
 ">On Spaces of Coverings</a>\nby Yuliy Baryshnikov (University of Illinois
  at Urbana-Champaign) as part of GEOTOP-A seminar\n\n\nAbstract\nConsider 
 a relation $R\\subset X\\times Y$ between two topological spaces. A finite
  collection $C=(x_1\,\\ldots\,x_n)\\in X^n$ is a covering if for any $y\\i
 n Y$\, one has  $(x_k\,y)\\in R$ for one of the points $x_k$ in  $C$. (For
  example\, if $X=Y$ is a metric space\, and $R$ is the relation of being a
 t the distance $<\\epsilon$\, then $C$ is a covering if the union of $\\ep
 silon$-balls around $x_k$'s cover $Y$.) The topology of the space of cover
 ings $C_R(n)$ is important\, if unexplored\, topic in several applied disc
 iplines\, from multi-agent systems to sociology. In this talk we discuss s
 ome examples where the homotopy type of these spaces can be explicitly com
 puted.\n
LOCATION:https://researchseminars.org/talk/GEOTOP-A/73/
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