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Coarse amenability versus paracompactness
Cencelj, Matija, 1958- ; Dydak, Jerzy ; Vavpetič, Aleš
Nedavne raziskave v grobi geometriji ali geometriji v velikem merilu so pokazale podobnosti med nekaterimi pojmi analize, geometrije v velikem merilu in topologije. Lastnost A, ki jo je vpeljal G. ...Yu, je grobi analogon amenabilnosti za grupe in za njeno posplošitev (eksaktni prostori) se je z razčlenitvami enote izkazalo, da je grobi analogon parakompaktnih prostorov. V članku poglobimo analogijo med grobo amenabilnostjo in parakompaktnostjo. Med drugim definiramo grobi analogon parakompaktnosti modeliran po karakterističnih lastnostih ekspanderjev. S to analogijo podamo enostavni dokaz, da so tri kategorije prostorov grobo neamenabilne: ekspanderji, prostori grafov z obodom, ki gre proti neskončnosti, in unije potenc končne netrivialne grupe.
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