Geodesic
Hyperspaces of universal curves and $2$-cells are true $F_{\sigma \delta }$-sets
Paweł Krupski 1
1 Mathematical Institute University of Wrocław Pl. Grunwaldzki 2/4 50-384 Wrocław, Poland
Colloquium Mathematicum, Tome 91 (2002) no. 1, pp. 91-98 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/cm91-1-7
Keywords: shown following hyperspaces endowed hausdorff metric absolute sigma delta sets cal sierpi ski universal curves locally compact metric space provided cal emptyset cal menger universal curves locally compact metric space provided cal emptyset cells plane

Paweł Krupski  1

1 Mathematical Institute University of Wrocław Pl. Grunwaldzki 2/4 50-384 Wrocław, Poland 
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Paweł Krupski. Hyperspaces of universal curves
and $2$-cells are true $F_{\sigma \delta }$-sets. Colloquium Mathematicum, Tome 91 (2002) no. 1, pp. 91-98. doi: 10.4064/cm91-1-7

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