1. CMB 2011 (vol 56 pp. 55)
 Bouziad, A.

Cliquishness and Quasicontinuity of TwoVariable Maps
We study the existence of continuity points for mappings
$f\colon X\times Y\to Z$ whose $x$sections $Y\ni y\to f(x,y)\in Z$ are
fragmentable and $y$sections $X\ni x\to f(x,y)\in Z$ are
quasicontinuous, where $X$ is a Baire space and $Z$
is a metric space. For the factor $Y$, we consider two
infinite ``pointpicking'' games $G_1(y)$ and $G_2(y)$ defined respectively
for each $y\in Y$ as follows: in the $n$th
inning, Player I gives a dense set $D_n\subset Y$, respectively, a dense open set $D_n\subset Y$. Then
Player II picks a point $y_n\in D_n$;
II wins if $y$ is in the closure of ${\{y_n:n\in\mathbb N\}}$, otherwise
I wins. It is shown that
(i) $f$ is
cliquish
if II has a winning strategy in $G_1(y)$ for every $y\in Y$, and (ii) $
f$ is quasicontinuous if
the $x$sections of $f$ are continuous and the set of $y\in Y$
such that II has a winning strategy in $G_2(y)$ is dense in $Y$. Item (i) extends substantially
a result of Debs and item (ii) indicates that
the problem of Talagrand on separately continuous maps has a positive answer for a wide
class of ``small'' compact spaces.
Keywords:cliquishness, fragmentability, joint continuity, pointpicking game, quasicontinuity, separate continuity, two variable maps Categories:54C05, 54C08, 54B10, 91A05 

2. CMB 2011 (vol 54 pp. 244)
 Daniel, D. ; Nikiel, J.; Treybig, L. B.; Tuncali, H. M.; Tymchatyn, E. D.

Homogeneous Suslinian Continua
A continuum is said to be Suslinian if it does not
contain uncountably many
mutually exclusive nondegenerate subcontinua. Fitzpatrick and
Lelek have shown that a metric Suslinian continuum $X$ has the
property that the set of points at which $X$ is connected im
kleinen is dense in $X$. We extend their result to Hausdorff Suslinian continua
and obtain a number of corollaries. In particular, we prove that a homogeneous,
nondegenerate, Suslinian continuum is a simple closed curve and that each separable,
nondegenerate, homogenous, Suslinian continuum is metrizable.
Keywords:connected im kleinen, homogeneity, Suslinian, locally connected continuum Categories:54F15, 54C05, 54F05, 54F50 

3. CMB 2008 (vol 51 pp. 570)
 Lutzer, D. J.; Mill, J. van; Tkachuk, V. V.

Amsterdam Properties of $C_p(X)$ Imply Discreteness of $X$
We prove, among other things, that if $C_p(X)$ is
subcompact in the sense of de Groot, then the space $X$ is
discrete. This generalizes a series of previous results on
completeness properties of function spaces.
Keywords:regular filterbase, subcompact space, function space, discrete space Categories:54B10, 54C05, 54D30 
