Asymptotic dimension of coarse spaces via maps to simplicial complexes
Cencelj, Matija, 1958- ; Dydak, Jerzy ; Vavpetič, Aleš
Znano je, da je parakompakten proctor ▫$X$▫ krovne dimenzije največ ▫$n$▫ natanko tedaj, ko se da vsako preslikavo ▫$f\colon X \to K$▫ iz ▫$X$▫ v simplicialni kompleks ▫$K$▫ potisniti v njegov ...▫$n$-▫skelet ▫$K^{(n)}$▫. To idejo uporabimo za karakterizacijo asimptotične dimenzije v grobi kategoriji poljubnih grobih prostorov. Zveznost preslikave ▫$f$▫ se nadomesti z variacijo ▫$f$▫ na elementih enakomerno omejenega pokritja. Na isti način se da posplošiti lastnost A G. Yuja na poljubne grobe prostore
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