We introduce the concept of logarithmic dimension of a compact set. In terms of this magnitude, the extension property and the diametral dimension of spaces $\calE(K)$ can be described for Cantor-type compact sets.

MSC Classifications:

46E10, 31A15, 46A04 show english descriptions Topological linear spaces of continuous, differentiable or analytic functions
Potentials and capacity, harmonic measure, extremal length [See also 30C85]
Locally convex Frechet spaces and (DF)-spaces 46E10 - Topological linear spaces of continuous, differentiable or analytic functions
31A15 - Potentials and capacity, harmonic measure, extremal length [See also 30C85]
46A04 - Locally convex Frechet spaces and (DF)-spaces

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