Hyperspaces of universal curves and -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.
