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  • A set in a separable metric space is called Borel-opaque if it meets every Borel set of positive topological dimension. We show that if there is a set of reals that is of cardinality the continuum and universal measure zero, then each separable space contains a Borel-opaque set that is of universal measure zero. Similar results hold for opaque sets that are perfectly meager, lambda sets etc., and can be extended to some nonseparable spaces. Using opacity we also construct universal measure zero sets of positive Hausdorff dimension.
  • A set in a separable metric space is called Borel-opaque if it meets every Borel set of positive topological dimension. We show that if there is a set of reals that is of cardinality the continuum and universal measure zero, then each separable space contains a Borel-opaque set that is of universal measure zero. Similar results hold for opaque sets that are perfectly meager, lambda sets etc., and can be extended to some nonseparable spaces. Using opacity we also construct universal measure zero sets of positive Hausdorff dimension. (en)
  • Množina v separabilním metrickém prostoru je borelovsky neprůhledná, pokud protíná každou borelovskou množinu kladné topologické dimenze. Ukazujeme, že existuje-li množina reálných čísel mohutnosti kontinua a univerzální míry nula, pak každý separabilní metrický prostor obsahuje je borelovsky neprůhlednou množinu univerzální míry nula. Podobné výsledky platí i pro jiné malé množiny. Pomocí neprůhlednosti konstruujeme množiny univerzální míry nula s kladnou Hausdorffovou dimenzí. (cs)
Title
  • Malé neprůhledné množiny (cs)
  • Small Opaque Sets
  • Small Opaque Sets (en)
skos:prefLabel
  • Malé neprůhledné množiny (cs)
  • Small Opaque Sets
  • Small Opaque Sets (en)
skos:notation
  • RIV/68407700:21110/03:01129160!RIV08-GA0-21110___
http://linked.open.../vavai/riv/strany
  • 455;469
http://linked.open...avai/riv/aktivita
http://linked.open...avai/riv/aktivity
  • P(GA201/00/0859)
http://linked.open...iv/cisloPeriodika
  • 2
http://linked.open...vai/riv/dodaniDat
http://linked.open...aciTvurceVysledku
http://linked.open.../riv/druhVysledku
http://linked.open...iv/duvernostUdaju
http://linked.open...titaPredkladatele
http://linked.open...dnocenehoVysledku
  • 627435
http://linked.open...ai/riv/idVysledku
  • RIV/68407700:21110/03:01129160
http://linked.open...riv/jazykVysledku
http://linked.open.../riv/klicovaSlova
  • opaque set; topological dimension; universal measure zero (en)
http://linked.open.../riv/klicoveSlovo
http://linked.open...odStatuVydavatele
  • US - Spojené státy americké
http://linked.open...ontrolniKodProRIV
  • [04B6928B9ADA]
http://linked.open...i/riv/nazevZdroje
  • Real Analysis Exchange
http://linked.open...in/vavai/riv/obor
http://linked.open...ichTvurcuVysledku
http://linked.open...cetTvurcuVysledku
http://linked.open...vavai/riv/projekt
http://linked.open...UplatneniVysledku
http://linked.open...v/svazekPeriodika
  • 28
http://linked.open...iv/tvurceVysledku
  • Zindulka, Ondřej
issn
  • 0147-1937
number of pages
http://localhost/t...ganizacniJednotka
  • 21110
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