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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