Hyperspaces of universal curves and 2-cells are true $F_{\sigma \delta }$-sets

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 -