Wojciech Bielas: An example of a rigid \(\kappa\)-superuniversal metric space
24/04/15 13:09
Tuesday, May 5, 2015 17:15
Room: D1-215
Speaker: Wojciech Bielas
Title: An example of a rigid \(\kappa\)-superuniversal metric space
Abstract. For an uncountable cardinal \(\kappa\) a metric space \(X\) is called to be \(\kappa\)-superuniversal if for every metric space \(Y\) with \(|Y | < \kappa\) every partial isometry from a subset of \(Y\) into \(X\) can be extended over the whole space \(Y\). It is easy to prove that if a \(\kappa\)-superuniversal metric space is of cardinality \(\kappa\), then it is also \(\kappa\)-homogeneous, i.e. every isometry of a subspace \(Y\) of the space with \(|Y | < \kappa\) can be extended to an isometry of the whole space. I will discuss an example of a \(\kappa\)-superuniversal metric space which has exactly one isometry.
Room: D1-215
Speaker: Wojciech Bielas
Title: An example of a rigid \(\kappa\)-superuniversal metric space
Abstract. For an uncountable cardinal \(\kappa\) a metric space \(X\) is called to be \(\kappa\)-superuniversal if for every metric space \(Y\) with \(|Y | < \kappa\) every partial isometry from a subset of \(Y\) into \(X\) can be extended over the whole space \(Y\). It is easy to prove that if a \(\kappa\)-superuniversal metric space is of cardinality \(\kappa\), then it is also \(\kappa\)-homogeneous, i.e. every isometry of a subspace \(Y\) of the space with \(|Y | < \kappa\) can be extended to an isometry of the whole space. I will discuss an example of a \(\kappa\)-superuniversal metric space which has exactly one isometry.