ACTA MATHEMATICA UNIVERSITATIS COMENIANAE
Vol. LXXIII, 1 (2004)
p. 1 – 20
Compactifications of Fractal Structures
F. G. Arenas and M. A. Sanchez-Granero
Abstract.
In this paper we introduce GF-compactifications, which are compactifications of
GF-spaces (a new notion introduced by the authors).
We study properties of this new kind of compactification and prove that every
GF-compactification is of Wallman type. We also prove that every metrizable compactification of a
metric space $X$ is a GF-compactification and, as a corollary, that every metric compactification
is of Wallman type, giving
a new proof of a result that dates back to Aarts.
Finally, we prove some extension theorems.
AMS Subject classification: 54D35;
Secondary: 54E15.
Keywords:
GF-space; metric compactification;
Wallman compactification.
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