Compressibility and Kolmogorov complexity (Q1934957)

In the paper under review, the authors investigated a metric space over \(2^{\omega}\) defined by \(d(x,y)=\overline{\lim}_n \frac{C(x\upharpoonright n|y\upharpoonright n)}{n}\). They prove that, among the others, for any \(\alpha\in [0,1]\), \(d(\alpha\cdot x, \alpha \cdot y)=\alpha\cdot d(x,y)\); and \(2^{\omega}\) is path connected.