Hyperspaces of universal curves and $2$-cells are true $F_{\sigma \delta }$-sets
Volume 91 / 2002
Colloquium Mathematicum 91 (2002), 91-98
MSC: Primary 54B20, 54F15; Secondary 54H05.
DOI: 10.4064/cm91-1-7
Abstract
It is shown that the following hyperspaces, endowed with the Hausdorff metric, are true absolute $F_{\sigma \delta }$-sets:
(1) ${\cal M}^2_1(X)$ of Sierpiński universal curves in a locally compact metric space $X$, provided ${\cal M}^2_1(X)\not =\emptyset $;
(2) ${\cal M}^3_1(X)$ of Menger universal curves in a locally compact metric space $X$, provided ${\cal M}^3_1(X)\not =\emptyset $;
(3) 2-cells in the plane.
