"US - Spojen\u00E9 st\u00E1ty americk\u00E9" . . "0002-9939" . . . . "Je uk\u00E1z\u00E1no, \u017Ee $F$-sigma aditivn\u00ED syst\u00E9m mno\u017Ein v \u00FApln\u00E9m metrick\u00E9m prostoru m\u00E1 $\\sigma$-diskr\u00E9tn\u00ED zjemn\u011Bn\u00ED."@cs . "$F\\sb \\sigma$-additive families and the invariance of Borel classes"@en . "522193" . . . "We prove that any $F_\\sigma$-additive family $\\A$ of sets in an absolutely Souslin metric space has a $\\sigma$-discrete refinement provided every partial selector set for $\\A$ is $\\sigma$-discrete. As a corollary we obtain that every mapping of a metric space onto an absolutely Souslin metric space, which maps $F_\\sigma$-sets to $F_\\sigma$-sets and has complete fibers, admits a section of the first class. The invariance of Borel and Souslin sets under mappings with complete fibers, which preserves $F_\\sigma$-sets, is shown as an application of the previous result." . "RIV/00216208:11320/05:00001384!RIV06-MSM-11320___" . "Proceedings of the American Mathematical Society" . "11"^^ . "$F$-sigma aditivn\u00ED syst\u00E9my mno\u017Ein a invariance borelovsk\u00FDch t\u0159\u00EDd"@cs . . "1"^^ . . "Spurn\u00FD, Ji\u0159\u00ED" . "$F\\sb \\sigma$-additive families and the invariance of Borel classes"@en . . . . "905;915" . . "1"^^ . "3" . "$F\\sb; \\sigma$-additive; families; invariance; Borel; classes"@en . "RIV/00216208:11320/05:00001384" . . . "P(GA201/03/0935), P(GP201/03/D120), Z(MSM 113200007)" . . "$F\\sb \\sigma$-additive families and the invariance of Borel classes" . "133" . . "$F\\sb \\sigma$-additive families and the invariance of Borel classes" . . . "$F$-sigma aditivn\u00ED syst\u00E9my mno\u017Ein a invariance borelovsk\u00FDch t\u0159\u00EDd"@cs . "[191D553B8861]" . . "11320" . . . "We prove that any $F_\\sigma$-additive family $\\A$ of sets in an absolutely Souslin metric space has a $\\sigma$-discrete refinement provided every partial selector set for $\\A$ is $\\sigma$-discrete. As a corollary we obtain that every mapping of a metric space onto an absolutely Souslin metric space, which maps $F_\\sigma$-sets to $F_\\sigma$-sets and has complete fibers, admits a section of the first class. The invariance of Borel and Souslin sets under mappings with complete fibers, which preserves $F_\\sigma$-sets, is shown as an application of the previous result."@en .