1. CJM 2015 (vol 68 pp. 675)
 MartínezdelaVega, Veronica; Mouron, Christopher

Monotone Classes of Dendrites
Continua $X$ and $Y$ are monotone equivalent
if there exist monotone onto maps $f:X\longrightarrow Y$ and
$g:Y\longrightarrow X$. A continuum $X$ is isolated with respect
to monotone maps if every continuum that is monotone equivalent
to $X$ must also be homeomorphic to
$X$. In this paper we show that a dendrite $X$ is isolated with
respect to
monotone maps if and only if the set of ramification points of
$X$ is
finite. In this way we fully characterize the classes of dendrites
that are
monotone isolated.
Keywords:dendrite, monotone, bqo, antichain Categories:54F50, 54C10, 06A07, 54F15, 54F65, 03E15 

2. CJM 2009 (vol 61 pp. 124)
 Dijkstra, Jan J.; Mill, Jan van

Characterizing Complete Erd\H os Space
The space now known as {\em complete Erd\H os
space\/} $\cerdos$ was introduced by Paul Erd\H os in 1940 as the
closed subspace of the Hilbert space $\ell^2$ consisting of all
vectors such that every coordinate is in the convergent sequence
$\{0\}\cup\{1/n:n\in\N\}$. In a solution to a problem posed by Lex G.
Oversteegen we present simple and useful topological
characterizations of $\cerdos$.
As an application we determine the class
of factors of $\cerdos$. In another application we determine
precisely which of the spaces that can be constructed in the Banach
spaces $\ell^p$ according to the `Erd\H os method' are homeomorphic
to $\cerdos$. A novel application states that if $I$ is a
Polishable $F_\sigma$ideal on $\omega$, then $I$ with the Polish
topology is homeomorphic to either $\Z$, the Cantor set $2^\omega$,
$\Z\times2^\omega$, or $\cerdos$. This last result answers a
question that was asked
by Stevo Todor{\v{c}}evi{\'c}.
Keywords:Complete Erd\H os space, Lelek fan, almost zerodimensional, nowhere zerodimensional, Polishable ideals, submeasures on $\omega$, $\R$trees, linefree groups in Banach spaces Categories:28C10, 46B20, 54F65 
