Every graph is a self-similar set.
External Characterization of I-Favorable Spaces
1991 AMS Math. Subj. Class.:Primary 54C10; Secondary 54F65We provide both a spectral and an internal characterizations of arbitrary !-favorable spaces with respect to co-zero sets. As a corollary we establish that any product of compact !-favorable spaces with respect to co-zero sets is also !-favorable with respect to co-zero sets. We also prove that every C* -embedded !-favorable with respect to co-zero sets subspace of an extremally disconnected space is extremally disconnected.
Extreme topological measures
It has been an open question since 1997 whether, and under what assumptions on the underlying space, extreme topological measures are dense in the set of all topological measures on the space. The present paper answers this question. The main result implies that extreme topological measures are dense on a variety of spaces, including spheres, balls and projective planes.