10 Dimension[0YH]

Let \((X,d)\) be a metric space. Let in the following \(K\) a compact non-empty subset of \(X\), and \(N(𝜌)\) the minimum number of balls of radius \(𝜌\) that are needed to cover \(K\).  ¹

Note that this definition depends a priori on the choice of the distance, i.e. \(N=N(𝜌,K,d)\) and \(\dim =\dim (K,d)\). See in particular [0YZ]↺↻.

E171

[0YK]↺↻

E171

[0YN]↺↻

E171

[0YQ]↺↻

E171

[0YS]↺↻

E171

[0YV]↺↻

E171

[0YX]↺↻

E171

[0YZ]↺↻

E171

[0Z1]↺↻

E171

[0Z3]↺↻

E171

[0Z7]↺↻

E171

[0ZB]↺↻

E171

[0ZD]↺↻

E171

[0ZG]↺↻

E171

[0ZJ]↺↻

E171

[0ZM]↺↻

E171

[0ZP]↺↻

E171

[0ZR]↺↻