Topological aspects of order in C(X)Kandić, Marko (Avtor) Vavpetič, Aleš (Avtor) vector latticescontinuous functionsseparation axiomsbands and projection bandsorder continuityun-convergenceIn 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 ▫$C_b(X)$▫.20192020-06-08 12:18:18Neznano116748UDK: 517.982.22:515.122ISSN pri članku: 1385-1292DOI: 10.1007/s11117-018-0628-8COBISS_ID: 18551897OceCobissID: 512122649sl