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- Ran_space abstract "In mathematics, the Ran space (or Ran's space) of a topological space X is a topological space whose underlying set is the set of all nonempty finite subsets of X: for a metric space X the topology is given by Hausdorff distance. The notion is named after Ziv Ran. It seems the notion was first introduced and popularized by A. Beilinson and V. Drinfeld, Chiral algebras.In general, the topology of the Ran space is generated by sets for any disjoint open subsets .A theorem of Beilinson and Drinfeld states that the Ran space of a connected manifold is weakly contractible.There is an analog of a Ran space for a scheme: the Ran prestack of a quasi-projective scheme X over a field k, denoted by , is the category where the objects are triples consisting of a finitely generated k-algebra R, a nonempty set S and a map of sets and where a morphism consists of a k-algebra homomorphism , a surjective map that commutes with and . Roughly, an R-point of is a nonempty finite set of R-rational points of X "with labels" given by . A theorem of Beilinson and Drinfeld continues to hold: is acyclic if X is connected.".
- Ran_space wikiPageExternalLink 1108.1741.pdf.
- Ran_space wikiPageExternalLink exponential_space.html.
- Ran_space wikiPageExternalLink LectureVIII-Poincare.pdf.
- Ran_space wikiPageID "42455846".
- Ran_space wikiPageRevisionID "605624698".
- Ran_space subject Category:Topological_spaces.
- Ran_space comment "In mathematics, the Ran space (or Ran's space) of a topological space X is a topological space whose underlying set is the set of all nonempty finite subsets of X: for a metric space X the topology is given by Hausdorff distance. The notion is named after Ziv Ran. It seems the notion was first introduced and popularized by A. Beilinson and V.".
- Ran_space label "Ran space".
- Ran_space sameAs m.0108884m.
- Ran_space sameAs Q17144166.
- Ran_space sameAs Q17144166.
- Ran_space wasDerivedFrom Ran_space?oldid=605624698.
- Ran_space isPrimaryTopicOf Ran_space.