1,366 research outputs found
On character of points in the Higson corona of a metric space
We prove that for an unbounded metric space , the minimal character
of a point of the Higson corona of is equal to
if has asymptotically isolated balls and to otherwise. This implies that under a
metric space of bounded geometry is coarsely equivalent to the Cantor
macro-cube 2^{<\IN} if and only if and . This contrasts with a result of Protasov saying that under CH
the coronas of any two asymptotically zero-dimensional unbounded metric
separable spaces are homeomorphic.Comment: 12 page
Spectra of Tukey types of ultrafilters on Boolean algebras
Extending recent investigations on the structure of Tukey types of
ultrafilters on to Boolean algebras in general, we
classify the spectra of Tukey types of ultrafilters for several classes of
Boolean algebras, including interval algebras, tree algebras, and pseudo-tree
algebras.Comment: 18 page
Combinatorial images of sets of reals and semifilter trichotomy
Using a dictionary translating a variety of classical and modern covering
properties into combinatorial properties of continuous images, we get a simple
way to understand the interrelations between these properties in ZFC and in the
realm of the trichotomy axiom for upward closed families of sets of natural
numbers. While it is now known that the answer to the Hurewicz 1927 problem is
positive, it is shown here that semifilter trichotomy implies a negative answer
to a slightly weaker form of this problem.Comment: Small update
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