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It is shown that the following hyperspaces, endowed with the Hausdorff metric, are true absolute -sets:
(1) ℳ ²₁(X) of Sierpiński universal curves in a locally compact metric space X, provided ℳ ²₁(X) ≠ ∅ ;
(2) ℳ ³₁(X) of Menger universal curves in a locally compact metric space X, provided ℳ ³₁(X) ≠ ∅ ;
(3) 2-cells in the plane.
Paweł Krupski. "Hyperspaces of universal curves and 2-cells are true $F_{σδ}$-sets." Colloquium Mathematicae 91.1 (2002): 91-98. <http://eudml.org/doc/283942>.
@article{PawełKrupski2002, abstract = {It is shown that the following hyperspaces, endowed with the Hausdorff metric, are true absolute $F_\{σδ\}$-sets:
(1) ℳ ²₁(X) of Sierpiński universal curves in a locally compact metric space X, provided ℳ ²₁(X) ≠ ∅ ;
(2) ℳ ³₁(X) of Menger universal curves in a locally compact metric space X, provided ℳ ³₁(X) ≠ ∅ ;
(3) 2-cells in the plane.}, author = {Paweł Krupski}, journal = {Colloquium Mathematicae}, keywords = {Borel set; hyperspace of continua; universal Menger continuum; universal Sierpiński continuum}, language = {eng}, number = {1}, pages = {91-98}, title = {Hyperspaces of universal curves and 2-cells are true $F_\{σδ\}$-sets}, url = {http://eudml.org/doc/283942}, volume = {91}, year = {2002}, }
TY - JOUR AU - Paweł Krupski TI - Hyperspaces of universal curves and 2-cells are true $F_{σδ}$-sets JO - Colloquium Mathematicae PY - 2002 VL - 91 IS - 1 SP - 91 EP - 98 AB - It is shown that the following hyperspaces, endowed with the Hausdorff metric, are true absolute $F_{σδ}$-sets:
(1) ℳ ²₁(X) of Sierpiński universal curves in a locally compact metric space X, provided ℳ ²₁(X) ≠ ∅ ;
(2) ℳ ³₁(X) of Menger universal curves in a locally compact metric space X, provided ℳ ³₁(X) ≠ ∅ ;
(3) 2-cells in the plane. LA - eng KW - Borel set; hyperspace of continua; universal Menger continuum; universal Sierpiński continuum UR - http://eudml.org/doc/283942 ER -