Wojciech Bielas

# Wojciech Bielas: An example of a rigid $$\kappa$$-superuniversal metric space

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.