**Research group in set
theoretic
topology and Boolean algebra**

Permanent
faculty
members: Bill Fleissner, Jack
Porter,
Judy Roitman

Advanced
graduate
students: Dan O'Neill

Recent PhD's: Jila Niknejad
2009, Lynne Yengulalp 2009, Nate Carlson 2006, Ellen Mir 2003

Seminar:
nearly every Monday

2:00 - 2:50

408 Snow Hall

For
pictures
from the Spring 2001 AMS Special Session in Set Theory, Topology, and
Boolean
Algebra, held at KU, click here
.

Faculty
research
interests

**William
Fleissner** started his research in set theory, in particular,
consistency
results in
general
topology. After focusing on the normal Moore
space conjecture
and
related topics,
he became interested in many areas of
set theoretic
topology. Recently,
he has studied "projective properties" --
for example, the
questions,
"If
all continuous Tychonoff images of space are
realcompact, must
the space
be
Lindelof?" and "What can be said about spaces all
of whose regular
images are
normal?"
Two topics of current research are
D-spaces and
subspaces of
the product
of finitely many ordinals.

**Jack
Porter's**
research is focused on spaces in which a
given space is
dense
(extensions),
and on the related notion of
absolutes (= Stone
space of
the
Boolean algebra of the regular open
sets). He is
also
interested
in spaces which are minimal with
respect to a
certain
property (for
example, a minimal Hausdorff space
has no Hausdorff
subtology)
or
maximal with respect to a certain
property (for
example, if
you extend
a compact topology by adding a
new open set, the
topology
is no
longer compact). The techniques
that he and his
colleague
Grant
Woods have developed in these areas
have turned out to
be
helpful in
a wide variety of topics in topology.

**Judith
Roitman** focused in the 1990's on Boolean algebras. The
topological
spaces

she looked at tend
to be closely related to Stone spaces of
Boolean
algebras. Here work
centered on
homomorphisms/continuous
maps, and on canonical
examples such as
Ostaszewski spaces
and Kunen lines. These two areas are
not unrelated.
Some recent
work
has been about almost disjoint families of
integers and the
Boolean
algebras
they generate, and (with Fleissner and Porter)
connected
subtopologies of
Hausdorff
spaces.
More recently she has been looking at

the old problem of the models in
which certain
box products are paracompact.