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.