Homotopski princip za submerzije s sprayem nad Steinovimi prostori : doktorska disertacija
Prezelj-Perman, Jasna
V prvem delu je dokazan homotopski princip za submerzije s sprayi: "Naj bo ▫$Z$▫ kompleksen prostor, ▫$X$▫ Steinov prostor, ▫$h: Z \to Z$▫ surjektivna holomorfna submerzija, ki lokalno dopušča spray, ...▫$P$▫ kompakten Hausdorffov prostor in ▫$a_p: X \to Z$▫, ▫$p \in P$▫, zvezna družina zveznih prerezov submerzije ▫$h: Z \to X$▫. Potem obstaja taka zvezna družina zveznih prerezov ▫$a_{p,t}: X \to Z$▫, ▫$p \in P$▫, ▫$t \in [0,1]$▫, da je ▫$a_{p,0} = a_p$▫, ▫$p \in P$▫ in je za vsak ▫$p \in P$▫ prerez ▫$a_{p,1}: X \to Z$▫ holomorfen." Glavni izrek v drugem delu je vložitveni izrek za Steinove mnogoterosti z interpolacijo na diskretnih množicah. "Naj bo ▫$X$▫ ▫$n$▫-dimenzionalna Steinova mnogoterost, ▫$Y \subset X$▫ diskretna podmnožica in ▫$\varphi: Y \to \Cc^{n+q}$▫ prava injekcija. Če je ▫$n=1$▫ in ▫$q \ge 2$▫ ali ▫$n>1$▫in ▫$q \ge \max \left{ \left[ \frac{n+1}{2} \right] + 1,3\right}$▫, obstaja pravaholomorfna vložitwv ▫$\Phi: X \to \Cc^{n+q}$▫, ki razširi ▫$\varphi$▫."
Type of material - dissertation
; adult, serious
Publication and manufacture - Ljubljana : [J. Prezelj], 2000
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