Daria Michalik: Symmetric products as cones
08/01/19 21:21
Tuesday, January 8, 2019 17:15
Room: D1-215
Speaker: Daria Michalik
Title: Symmetric products as cones
Abstract. (join work with Alejandro Illanes and Veronica Martinez-de-la-Vega)
For a continuum \(X\), let \(F_n(X)\) be the hyperspace of all nonempty subsets of \(X\)with at most \(n\)-points. The space \(F_n(X)\) is called the n'th-symmetric product.
In [1] it was proved that if \(X\)is a cone, then its hyperspace \(F_n(X)\) is also a cone.
During my talk I will discuss the converse problem. I will prove that if \(X\)is a locally connected curve, then the following conditions are equivalent:
[1] A. Illanes, V. Martinez-de-la-Vega, Symmetric products as cones, Topology Appl. 228 (2017), 36–46.
Room: D1-215
Speaker: Daria Michalik
Title: Symmetric products as cones
Abstract. (join work with Alejandro Illanes and Veronica Martinez-de-la-Vega)
For a continuum \(X\), let \(F_n(X)\) be the hyperspace of all nonempty subsets of \(X\)with at most \(n\)-points. The space \(F_n(X)\) is called the n'th-symmetric product.
In [1] it was proved that if \(X\)is a cone, then its hyperspace \(F_n(X)\) is also a cone.
During my talk I will discuss the converse problem. I will prove that if \(X\)is a locally connected curve, then the following conditions are equivalent:
- \(X\)is a cone,
- \(F_n(X)\) is a cone for some \(n\ge 2\),
- \(F_n(X)\) is a cone for each \(n\ge 2\).
[1] A. Illanes, V. Martinez-de-la-Vega, Symmetric products as cones, Topology Appl. 228 (2017), 36–46.