20.500.12556/RUL-109543 On the Alexandroff-Borsuk problem O problemu Aleksandrova in Borsuka We investigate the classical Alexandroff-Borsuk problem in the category of non-triangulable manifolds: Given an ▫$n$▫-dimensional compact non-triangulable manifold ▫$M^n$▫ and ▫$\varepsilon > 0$▫, does there exist an ▫$\varepsilon$▫-map of ▫$M^n$▫ onto an ▫$n$▫-dimensional finite polyhedron which induces a homotopy equivalence? Obravnavamo klasični problem Aleksandrova in Borsuka v kategoriji netriangulabilnih mnogoterosti: ali za dano ▫$n$▫-dimenzionalno kompaktno netriangulabilno mnogoterost ▫$M^n$▫ in dani ▫$\varepsilon > 0$▫ obstaja ▫$\varepsilon$▫-preslikava ▫$M^n$▫ na ▫$n$▫-dimenzionalni končni polieder, ki inducira homotopsko ekvivalenco? ANR finite polyhedron homotopy equivalence ▫$\varepsilon$▫-map cellular map almost-smooth manifold ▫$|E_8|$▫-manifold Kirby-Siebenmann class Galewski-Stern obstruction non-triangulable manifold Alexandroff-Borsuk Manifold Problem ANR končni polieder homotopska ekvivalenca ▫$\varepsilon$▫-preslikava celularna preslikava skoraj gladka mnogoterost $|E_8|$-mnogoterost Kirby-Siebenmannov razred Galewski-Sternova ovira netriangulabilna mnogoterost problem Aleksandrova in Borsuka o mnogoterostih true false true Angleški jezik Slovenski jezik Članek v reviji 2019-09-05 12:50:06 2019-09-05 12:50:07 2022-08-21 03:42:50 0000-00-00 00:00:00 2017 0 0 Str. 114-120 Vol. 221 2017 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 515.12 0166-8641 http://dx.doi.org/10.1016/j.topol.2017.02.052 17958233 26538752 RAZ_Cencelj_Matija_i2017.pdf RAZ_Cencelj_Matija_i2017.pdf 1 21FD21EBF257CCA9492A3182A224843A d9120f6d31f5573d530cf2d8505d011bfcb04fa68ee947ad193ffb3299dbf362 e44d90d1-a1b6-11eb-a523-00155dcfd717 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=121121 Pedagoška fakulteta Fakulteta za matematiko in fiziko 0 0 0