20.500.12556/RUL-116748 Topological aspects of order in C(X) Topološki vidiki urejenosti v C(X) In this paper we consider the relationship between order and topology in the vector lattice ▫$C(X)$▫ of all continuous functions on a Hausdorff space ▫$X$▫. We prove that the restriction of ▫$f\in C(X)$▫ to a closed set ▫$A$▫ in the case when ▫$X\in T_{3 \frac 12}$▫ induces an order continuous operator iff ▫$A= \overline{\mathrm{Int\,}A}.$▫ This result enables us to easily characterize bands and projection bands in ▫$C_0(X)$▫, ▫$C_b(X)$▫ and ▫$C(X)$▫. Our results serve us to provide a positive answer to the question on lifting un-convergence from closed ideals of ▫$C_0(X)$▫ and ▫$C_b(X)$▫. Obravnavamo povezavo med urejenostjo in topologijo v mreži ▫$C(X)$▫ zveznih funkcij na Hausdorffovem prostoru ▫$X$▫. Dokažemo, da zožitev funkcije ▫$f\in C(X)$▫ na zaprto podmnožico ▫$A$▫ v primeru, ko je ▫$X\in T_{3\frac{1}{2}}$▫, inducira urejenostno zvezen operator natanko takrat, ko je ▫$A=\overline{\mathrm{Int\,}A}$▫. S tem rezultatom na enostaven način karakteriziramo pasove in projekcijske pasove v ▫$C_0(X)$▫, ▫$C_b(X)$▫ in ▫$C(X)$▫. Z dobljenimi rezultati podamo pozitiven odgovor na vprašanje o dvigu un-konvergence z zaprtih idealov mrež ▫$C_0(X)$▫ in ▫$C_b(X)$▫. vector lattices continuous functions separation axioms bands and projection bands order continuity un-convergence vektorske mreže zvezne funkcije separacijski aksiomi pasovi in projekcijski pasovi urejenostna zveznost un-konvergenca true false false Angleški jezik Slovenski jezik Neznano 2020-06-08 12:18:18 2020-06-08 12:18:22 2022-08-29 03:38:54 0000-00-00 00:00:00 2019 0 0 Str. 617-635 iss. 3 Vol. 23 July 2019 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 517.982.22:515.122 1385-1292 10.1007/s11117-018-0628-8 18551897 512122649 RAZ_Kandic_Marko_2019.pdf RAZ_Kandic_Marko_2019.pdf 1 D9611443793E4BE035F10A5132FFD799 e8036f440163d653844900b6a9834b738b1dbee16f94a3af4151f11d5862d4d9 005e4216-a1b9-11eb-a523-00155dcfd717 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=130422 Fakulteta za matematiko in fiziko 0 0 0