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1. CMB Online first
Characters on $C( X)$ The precise condition on a completely regular space $X$ for every character on
$C(X) $ to be an evaluation at some point in $X$ is that $X$ be
realcompact. Usually, this classical result is obtained relying heavily on
involved (and even nonconstructive) extension arguments. This note provides a
direct proof that is accessible to a large audience.
Keywords:characters, realcompact, evaluation, real-valued continuous functions Categories:54C30, 46E25 |
2. CMB 2011 (vol 56 pp. 292)
Quasisymmetrically Minimal Moran Sets M. Hu and S. Wen considered quasisymmetrically minimal uniform Cantor
sets of Hausdorff dimension $1$, where at the $k$-th set one removes
from each interval $I$ a certain number $n_{k}$ of open subintervals
of length $c_{k}|I|$, leaving $(n_{k}+1)$ closed subintervals of
equal length. Quasisymmetrically Moran sets of Hausdorff dimension $1$
considered in the paper are more general than uniform Cantor sets in
that neither the open subintervals nor the closed subintervals are
required to be of equal length.
Keywords:quasisymmetric, Moran set, Hausdorff dimension Categories:28A80, 54C30 |
3. CMB 2009 (vol 52 pp. 295)
On Functions Whose Graph is a Hamel Basis, II We say that a function $h \from \real \to \real$ is a Hamel function
($h \in \ham$) if $h$, considered as a subset of $\real^2$, is a Hamel
basis for $\real^2$. We show that $\A(\ham)\geq\omega$, \emph{i.e.,} for
every finite $F \subseteq \real^\real$ there exists $f\in\real^\real$
such that $f+F \subseteq \ham$. From the previous work of the author
it then follows that $\A(\ham)=\omega$.
Keywords:Hamel basis, additive, Hamel functions Categories:26A21, 54C40, 15A03, 54C30 |