Homotopski princip za submerzije s sprayem nad Steinovimi prostori - Prezelj-Perman, Jasna (visokošolska dela, 2000)
The first part contains a proof of the homotopy principle for holomorphic submersions with sprays: "Let ?$Z$? be a complex space, ?$X$? Stein space, ?$h: Z → Z$? surjective holomorphic submersion which locally admits a spray, ?$P$? a compact Hausdorff space and ?$a_p: X → Z$?, ?$p \in P$?, a continuous family of continuous sections of submersion ?$h: Z → X$?. Then there exist a continuous family of continuous sections ?$a_{p,t}: X → Z$?, ?$p \in P$?, ?$t \in 0,1$?, of ?$h: Z → X$?, such that ?$a_{p,0} = a_p$?, ?$p \in P$? and the section ?$a_{p,1}: X → Z$? is holomorphic for each ?$p \in P$?." The second part is an embedding theorem for Stein manifolds with interpolation on discrete sets. "Let ?$X$? be an ?$n$?-dimensional Stein manifold, ?$Y \subset X$? a discrete subset and ?$φ: Y → \Cc^{n+q}$? a proper injective map. If ?$n=1$? and ?$q \ge 2$? or ?$n>1$? and ?$q \ge \max \left{ \left \frac{n+1}{2} \right + 1,3 \right}$? then there exist a proper holomorphic enbedding ?$Φ: X → \Cc^{n+q}$? extending ?$φ$?."
Keywords: Steinov prostor; Disertacije; kompleksna analiza; kompleksni prostor; holomorfna submerzija; holomorfni prerez; tangentni prostor; homotopski principi; holomorfna vložitev