FEBRUARY 27: Wistar Comfort (Wesleyan University),
"Some Unresolved Irresolvability Issues". At Queens College, Tea 3:15 pm, Keily 508;
Talk 4:00 pm, Keily 119B.
For information, parking: G. Itzkowitz: zev@forbin.qc.edu,
(718)997-5849.
ABSTRACT: Following Edwin Hewitt (1943), one says that a topological
space is resolvable [resp., kappa--resolvable] if it admits two [resp.,
kappa--many] disjoint dense subsets. I will attempt to summarize several
lines of investigation pursued over the years by many investigators.
Sample results due to Malykhin, Protasov, Zelenyuk and others are:
1. Every infinite Abelian group G not containing the countably infinite
Boolean group contains two disjoint sets, both dense in each nondiscrete
group topology on G.
2. Every infinite group G contains |G|--many disjoint sets, each dense in
each maximally almost periodic group topology on G.
3. Every countably compact, dense-in-itself regular Hausdorff space is
resolvable.
The emphasis will be on unsolved problems (the "unresolved
irresolvability issues").
Remark. My own efforts will be cited as time permits. Co-authors include
Jan van Mill, Li Feng, Oscar Masaveu, Hao Zhou, Salvador Garcia-Ferreira,
and Wanjun Hu.
MARCH 6: No seminar.
MARCH 13: Melvin Henriksen, "A survey of what we know and don't know about spaces X
for which the ring C(X) of continuous real-valued functions has a compact space of minimal
prime ideals". At Baruch College, Tea 3:15 pm, Talk 4:00 pm, Conference Room (6-215),
Mathematics, 6th floor, Vertical Campus, Lexington Avenue and 24th Street.
Contact: A. R. Todd: artbb@cunyvm.cuny.edu, (646) 312-4136.
ABSTRACT: There are characterizations of such spaces that are not easy to
use. This class includes all metrizable and all separable spaces, but not
all that are first countable. The Stone-Cech compactification betaD of
discrete space D has this property has this property, but betaD \ D does
not if D is infinite Topics like when this property is finitely
productive, what kinds of subspaces inherit it, and under what kinds of
mappings it is preserved are discussed. There are lots of open questions.
MARCH 20: No seminar -- Spring Topology Conference in Texas!