20.500.12556/RUL-118691 Ekstremno nepovezani prostori delo diplomskega seminarja Extremally disconnected spaces Ekstremno nepovezani prostori so prostori, v katerih je zaprtje vsake odprte množice odprta množica. V tem diplomskem delu se osredotočimo na nekatere zanimive lastnosti ekstremno nepovezanih prostorov Tihonova. Pokažemo, da je v takšnih prostorih vsako konvergentno zaporedje od nekega člena naprej konstantno. Doka- žemo, da je prostor Tihonova ekstremno nepovezan natanko tedaj, ko ima vsaka navzgor omejena podmnožica delno urejene množice C(X) natančno zgornjo mejo. Pokažemo tudi, da je za prostore Tihonova vsako ekstremno nepovezano topološko polje diskretno in da je topološka grupa diskretna natanko tedaj, ko je prostor G×G ekstremno nepovezan. Na koncu s pomočjo Stone-Čechove kompaktifikacije najdemo primer prostorov, ki jih preučujemo. Extremally disconnected spaces are spaces, in which the closure of every open set is open. In this thesis we examine some interesting properties of extremally disconnec- ted Tychonoff spaces. We prove that in such spaces, every convergent sequence is constant from some point on. We show that a Tychonoff space is extremally disco- nected if and only if every subset of the partially ordered set C(X) that has an upper bound, also has a least upper bound. We also prove that an extremally disconnected Tychonoff topological field is discrete and that an extremally disconnected Tycho- noff topological group G is discrete if and only if the product G × G is extremally disconnected. In the end of this thesis we define Stone-Cech compactification in order to find an example of the spaces that we are studying. ekstremno nepovezan prostor topološke grupe topološka polja Stone-Čechova kompaktifikacija extremally disconnected space topological group topological field Stone-Čech compactification true false false Slovenski jezik Angleški jezik Delo diplomskega seminarja/zaključno seminarsko delo/naloga 2020-08-30 08:15:02 2020-08-30 08:15:04 2024-05-30 10:11:33 0000-00-00 00:00:00 2020 0 0 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 515.1 107979 58825987 1346.pdf 1346.pdf 1 589F89952929665DCFB18D97B4A1CEE0 a82535987740e9f299feb61a6da17c63ed34aa527c2dd3ebee913d840e5c32a4 8f3e82e6-a1b9-11eb-a523-00155dcfd717 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=133079 Fakulteta za matematiko in fiziko 0 0 0